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diff --git a/interpolation.py b/interpolation.py
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index 0000000000000000000000000000000000000000..a04307d4fd07fdcfdd1010bb3ef8aa9b14695844
--- /dev/null
+++ b/interpolation.py
@@ -0,0 +1,144 @@
+import numpy as np
+import os
+import glob
+import motmetrics as mm
+
+from tracking_utils.evaluation import Evaluator
+
+
+def mkdir_if_missing(d):
+    if not os.path.exists(d):
+        os.makedirs(d)
+
+
+def eval_mota(data_root, txt_path):
+    accs = []
+    seqs = sorted([s for s in os.listdir(data_root) if s.endswith('FRCNN')])
+    #seqs = sorted([s for s in os.listdir(data_root)])
+    for seq in seqs:
+        video_out_path = os.path.join(txt_path, seq + '.txt')
+        evaluator = Evaluator(data_root, seq, 'mot')
+        accs.append(evaluator.eval_file(video_out_path))
+    metrics = mm.metrics.motchallenge_metrics
+    mh = mm.metrics.create()
+    summary = Evaluator.get_summary(accs, seqs, metrics)
+    strsummary = mm.io.render_summary(
+        summary,
+        formatters=mh.formatters,
+        namemap=mm.io.motchallenge_metric_names
+    )
+    print(strsummary)
+
+
+def get_mota(data_root, txt_path):
+    accs = []
+    seqs = sorted([s for s in os.listdir(data_root) if s.endswith('FRCNN')])
+    #seqs = sorted([s for s in os.listdir(data_root)])
+    for seq in seqs:
+        video_out_path = os.path.join(txt_path, seq + '.txt')
+        evaluator = Evaluator(data_root, seq, 'mot')
+        accs.append(evaluator.eval_file(video_out_path))
+    metrics = mm.metrics.motchallenge_metrics
+    mh = mm.metrics.create()
+    summary = Evaluator.get_summary(accs, seqs, metrics)
+    strsummary = mm.io.render_summary(
+        summary,
+        formatters=mh.formatters,
+        namemap=mm.io.motchallenge_metric_names
+    )
+    mota = float(strsummary.split(' ')[-6][:-1])
+    return mota
+
+
+def write_results_score(filename, results):
+    save_format = '{frame},{id},{x1},{y1},{w},{h},{s},-1,-1,-1\n'
+    with open(filename, 'w') as f:
+        for i in range(results.shape[0]):
+            frame_data = results[i]
+            frame_id = int(frame_data[0])
+            track_id = int(frame_data[1])
+            x1, y1, w, h = frame_data[2:6]
+            score = frame_data[6]
+            line = save_format.format(frame=frame_id, id=track_id, x1=x1, y1=y1, w=w, h=h, s=-1)
+            f.write(line)
+
+
+def dti(txt_path, save_path, n_min=25, n_dti=20):
+    seq_txts = sorted(glob.glob(os.path.join(txt_path, '*.txt')))
+    for seq_txt in seq_txts:
+        print(seq_txt)
+        seq_name = seq_txt.split('\\')[-1]
+        seq_data = np.loadtxt(seq_txt, dtype=np.float64, delimiter=',')
+        min_id = int(np.min(seq_data[:, 1]))
+        max_id = int(np.max(seq_data[:, 1]))
+        seq_results = np.zeros((1, 10), dtype=np.float64)
+        for track_id in range(min_id, max_id + 1):
+            index = (seq_data[:, 1] == track_id)
+            tracklet = seq_data[index]
+            tracklet_dti = tracklet
+            if tracklet.shape[0] == 0:
+                continue
+            n_frame = tracklet.shape[0]
+            n_conf = np.sum(tracklet[:, 6] > 0.5)
+            if n_frame > n_min:
+                frames = tracklet[:, 0]
+                frames_dti = {}
+                for i in range(0, n_frame):
+                    right_frame = frames[i]
+                    if i > 0:
+                        left_frame = frames[i - 1]
+                    else:
+                        left_frame = frames[i]
+                    # disconnected track interpolation
+                    if 1 < right_frame - left_frame < n_dti:
+                        num_bi = int(right_frame - left_frame - 1)
+                        right_bbox = tracklet[i, 2:6]
+                        left_bbox = tracklet[i - 1, 2:6]
+                        for j in range(1, num_bi + 1):
+                            curr_frame = j + left_frame
+                            curr_bbox = (curr_frame - left_frame) * (right_bbox - left_bbox) / \
+                                        (right_frame - left_frame) + left_bbox
+                            frames_dti[curr_frame] = curr_bbox
+                num_dti = len(frames_dti.keys())
+                if num_dti > 0:
+                    data_dti = np.zeros((num_dti, 10), dtype=np.float64)
+                    for n in range(num_dti):
+                        data_dti[n, 0] = list(frames_dti.keys())[n]
+                        data_dti[n, 1] = track_id
+                        data_dti[n, 2:6] = frames_dti[list(frames_dti.keys())[n]]
+                        data_dti[n, 6:] = [1, -1, -1, -1]
+                    tracklet_dti = np.vstack((tracklet, data_dti))
+            seq_results = np.vstack((seq_results, tracklet_dti))
+        save_seq_txt = os.path.join(save_path, seq_name)
+        seq_results = seq_results[1:]
+        seq_results = seq_results[seq_results[:, 0].argsort()]
+        write_results_score(save_seq_txt, seq_results)
+
+
+if __name__ == '__main__':
+    data_root = 'D:/dataset/tracking/mot/MOT17/train'
+    txt_path = './results/bytetrack'
+    save_path = './results/dti_bytetrack'
+    
+    mkdir_if_missing(save_path)
+    dti(txt_path, save_path, n_min=5, n_dti=20)
+    print('Before DTI: ')
+    eval_mota(data_root, txt_path)
+    print('After DTI:')
+    eval_mota(data_root, save_path)
+
+    '''
+    mota_best = 0.0
+    best_n_min = 0
+    best_n_dti = 0
+    for n_min in range(5, 50, 5):
+        for n_dti in range(5, 30, 5):
+            dti(txt_path, save_path, n_min, n_dti)
+            mota = get_mota(data_root, save_path)
+            if mota > mota_best:
+                mota_best = mota
+                best_n_min = n_min
+                best_n_dti = n_dti
+                print(mota_best, best_n_min, best_n_dti)
+    print(mota_best, best_n_min, best_n_dti)
+    '''
diff --git a/matlab/MOT16-04_f50.txt b/matlab/MOT16-04_f50.txt
new file mode 100644
index 0000000000000000000000000000000000000000..561c3fc5611ebeb9d78f7aac53e40937a6bb3817
--- /dev/null
+++ b/matlab/MOT16-04_f50.txt
@@ -0,0 +1,42 @@
+9.565844535827636719e-01
+9.517722129821777344e-01
+9.434401988983154297e-01
+9.424381256103515625e-01
+9.416198730468750000e-01
+9.410023689270019531e-01
+9.409747123718261719e-01
+9.400548934936523438e-01
+9.395396709442138672e-01
+9.395112991333007812e-01
+9.385929107666015625e-01
+9.370722770690917969e-01
+9.370422363281250000e-01
+9.365844726562500000e-01
+9.360661506652832031e-01
+9.341764450073242188e-01
+9.327757358551025391e-01
+9.327137470245361328e-01
+9.303717613220214844e-01
+9.293007850646972656e-01
+9.288790225982666016e-01
+9.283590316772460938e-01
+9.274177551269531250e-01
+9.274177551269531250e-01
+9.259564876556396484e-01
+9.250500202178955078e-01
+9.210121631622314453e-01
+9.192106723785400391e-01
+9.191372394561767578e-01
+9.113438129425048828e-01
+9.111337661743164062e-01
+9.097912311553955078e-01
+9.078912734985351562e-01
+9.035503864288330078e-01
+8.958532810211181641e-01
+8.923974037170410156e-01
+8.894762992858886719e-01
+8.453242778778076172e-01
+8.178932666778564453e-01
+7.879743576049804688e-01
+5.580991506576538086e-02
+1.418828219175338745e-02
diff --git a/matlab/MOT16-13_f250.txt b/matlab/MOT16-13_f250.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c8f1dca2092b6a39518dfaedf0009b7f9b186759
--- /dev/null
+++ b/matlab/MOT16-13_f250.txt
@@ -0,0 +1,17 @@
+9.231376647949218750e-01
+9.084212779998779297e-01
+8.954236507415771484e-01
+8.653736114501953125e-01
+8.527493476867675781e-01
+8.514318466186523438e-01
+8.464326858520507812e-01
+8.067240715026855469e-01
+8.008511066436767578e-01
+7.963542938232421875e-01
+7.894668579101562500e-01
+7.821791172027587891e-01
+7.812211513519287109e-01
+7.782025337219238281e-01
+2.001374959945678711e-02
+1.751923561096191406e-02
+1.539498567581176758e-02
diff --git a/matlab/MOT20-01_f100.txt b/matlab/MOT20-01_f100.txt
new file mode 100644
index 0000000000000000000000000000000000000000..99930d01673a935a2eeb36c33d621c8dd8bcd2c4
--- /dev/null
+++ b/matlab/MOT20-01_f100.txt
@@ -0,0 +1,52 @@
+9.444153308868408203e-01
+9.356088638305664062e-01
+9.274177551269531250e-01
+9.190618991851806641e-01
+9.141454696655273438e-01
+9.136986732482910156e-01
+9.109783172607421875e-01
+9.108152389526367188e-01
+9.098405838012695312e-01
+9.022235870361328125e-01
+9.012508392333984375e-01
+8.986320495605468750e-01
+8.971700668334960938e-01
+8.952698707580566406e-01
+8.942956924438476562e-01
+8.929824829101562500e-01
+8.923473358154296875e-01
+8.913221359252929688e-01
+8.842804431915283203e-01
+8.840517997741699219e-01
+8.767604827880859375e-01
+8.763313293457031250e-01
+8.762733936309814453e-01
+8.762149810791015625e-01
+8.751568794250488281e-01
+8.690760135650634766e-01
+8.656206130981445312e-01
+8.575077056884765625e-01
+8.571875095367431641e-01
+8.570568561553955078e-01
+8.489964008331298828e-01
+8.476126194000244141e-01
+8.457322120666503906e-01
+8.337223529815673828e-01
+8.313088417053222656e-01
+8.121414184570312500e-01
+6.521019935607910156e-01
+2.681844234466552734e-01
+1.945304870605468750e-01
+1.870610713958740234e-01
+1.723705530166625977e-01
+1.335558891296386719e-01
+1.020963191986083984e-01
+9.320765733718872070e-02
+7.383191585540771484e-02
+6.535232067108154297e-02
+4.063281416893005371e-02
+3.458574414253234863e-02
+2.754360437393188477e-02
+1.850811392068862915e-02
+1.356884837150573730e-02
+1.195202767848968506e-02
diff --git a/matlab/draw_conf.m b/matlab/draw_conf.m
new file mode 100644
index 0000000000000000000000000000000000000000..91276cacf7c1278646d211305b970fdaf5f10bd3
--- /dev/null
+++ b/matlab/draw_conf.m
@@ -0,0 +1,41 @@
+headerlinesIn = 0;
+delimiterIn = '';
+
+MOT16_04_f50 = importdata("MOT16-04_f50.txt", delimiterIn, headerlinesIn);
+MOT16_13_f250 = importdata("MOT16-13_f250.txt", delimiterIn, headerlinesIn);
+MOT20_01_f100 = importdata("MOT20-01_f100.txt", delimiterIn, headerlinesIn);
+
+figure;
+subplot(3,1,1);
+plot(1:size(MOT16_04_f50,1),MOT16_04_f50)
+title('MOT16-04, Frame 50');
+xlabel('Detection');
+ylabel('Conf. Score');
+[~, argmin] = min(diff(MOT16_04_f50));
+hold on;
+plot(argmin, MOT16_04_f50(argmin), 'ro');
+
+hold on;
+subplot(3,1,2); 
+plot(1:size(MOT16_13_f250,1),MOT16_13_f250)
+title('MOT16-13, Frame 250');
+xlabel('Detection');
+ylabel('Conf. Score');
+[~, argmin] = min(diff(MOT16_13_f250));
+hold on;
+plot(argmin, MOT16_13_f250(argmin), 'ro');
+
+hold on;
+subplot(3,1,3); 
+plot(1:size(MOT20_01_f100,1),MOT20_01_f100)
+title('MOT20-01, Frame 100');
+xlabel('Detection');
+ylabel('Conf. Score');
+[~, argmin] = min(diff(MOT20_01_f100));
+hold on;
+plot(argmin, MOT20_01_f100(argmin), 'ro');
+
+set(gcf, 'Color', 'w');
+addpath(genpath('./export_fig'));
+%export_fig conf_selection.pdf; % https://github.com/altmany/export_fig
+
diff --git a/matlab/draw_results.m b/matlab/draw_results.m
new file mode 100644
index 0000000000000000000000000000000000000000..93fe814ad629bfff67e13466a4a94b815d83bdfb
--- /dev/null
+++ b/matlab/draw_results.m
@@ -0,0 +1,50 @@
+figure;
+subplot(3,1,1);
+conf = [0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8];
+fix_conf_idf1 = [76.5 78.1 80.0 80.4 81.6 81.9 71.1];
+fix_conf_mota = [83.3 84.6 85.7 86.3 86.4 84.0 64.3];
+fix_conf_ids = [826 731 645 564 425 294 106];
+plot(conf, fix_conf_idf1, 'r-*'); hold on;
+plot(conf, ones(size(conf)) * 81.3, 'r-');
+plot(conf, fix_conf_mota, 'b-.*'); hold on;
+plot(conf, ones(size(conf)) * 86.3, 'b-.');
+xlim([min(conf), max(conf)]);
+xlabel('Confidence Score');
+ylabel('Performance in Percentage');
+legend('Fixed Conf. IDF1', 'Adaptive Conf. IDF1', 'Fixed Conf. MOTA', 'Adaptive Conf. MOTA');
+title('Evaluation Comparion on MOT16 Dataset');
+hold on;
+subplot(3,1,2);
+conf = [0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8];
+fix_conf_idf1 = [76.7 78.4 80.2 80.6 81.9 81.7 70.5];
+fix_conf_mota = [84.8 86.0 87.1 87.6 87.4 84.2 63.6];
+fix_conf_ids = [2613 2292 2007 1740 1308 909 324];
+plot(conf, fix_conf_idf1, 'r-*'); hold on;
+plot(conf, ones(size(conf)) * 81.5, 'r-');
+plot(conf, fix_conf_mota, 'b-.*'); hold on;
+plot(conf, ones(size(conf)) * 87.5, 'b-.');
+xlim([min(conf), max(conf)]);
+xlabel('Confidence Score');
+ylabel('Performance in Percentage');
+legend('Fixed Conf. IDF1', 'Adaptive Conf. IDF1', 'Fixed Conf. MOTA', 'Adaptive Conf. MOTA');
+title('Evaluation Comparion on MOT17 Dataset');
+hold on;
+subplot(3,1,3);
+conf = [0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8];
+fix_conf_idf1 = [80.9 81.2 81.7 81.9 81.9 81.7 60.8];
+fix_conf_mota = [78.5 79.0 79.2 79.4 78.9 78.9 53.0];
+fix_conf_ids = [2003 1599 1291 1129 1050 934 560];
+plot(conf, fix_conf_idf1, 'r-*'); hold on;
+plot(conf, ones(size(conf)) * 81.6, 'r-');
+plot(conf, fix_conf_mota, 'b-.*'); hold on;
+plot(conf, ones(size(conf)) * 79.4, 'b-.');
+xlim([min(conf), max(conf)]);
+xlabel('Confidence Score');
+ylabel('Performance in Percentage');
+legend('Fixed Conf. IDF1', 'Adaptive Conf. IDF1', 'Fixed Conf. MOTA', 'Adaptive Conf. MOTA');
+title('Evaluation Comparion on MOT20 Dataset');
+
+set(gcf, 'Color', 'w');
+addpath(genpath('./export_fig'));
+%export_fig conf_selection.pdf; % https://github.com/altmany/export_fig
+
diff --git a/matlab/example.py b/matlab/example.py
new file mode 100644
index 0000000000000000000000000000000000000000..9c17bffe9ab3babb8d5ec87bedff38a4a81c85f0
--- /dev/null
+++ b/matlab/example.py
@@ -0,0 +1,14 @@
+import numpy as np
+
+
+def descent(X, y, learning_rate=0.001, iters=100):
+    w = np.zeros((X.shape[1], 1))
+    for i in range(iters):
+        grad_vec = -(X.T).dot(y - X.dot(w))
+        w = w - learning_rate * grad_vec
+    return w
+
+
+X = np.loadtxt("MOT16-13_f250.txt")
+print(X)
+# grad_vec = -(X.T).dot(y - X.dot(w))
diff --git a/mot_evaluator.py b/mot_evaluator.py
new file mode 100644
index 0000000000000000000000000000000000000000..522272b85134616ff5f7717e56a8bb8a4b857f29
--- /dev/null
+++ b/mot_evaluator.py
@@ -0,0 +1,375 @@
+from loguru import logger
+
+from trackers.bytetrack.byte_tracker import BYTETracker
+
+import os
+import numpy as np
+import cv2
+import glob
+import os.path as osp
+import time
+from tracking_utils.evaluation import Evaluator
+import motmetrics as mm
+import trackeval
+import sys
+
+def write_results(filename, results):
+    save_format = '{frame},{id},{x1},{y1},{w},{h},{s},-1,-1,-1\n'
+    with open(filename, 'w') as f:
+        for frame_id, tlwhs, track_ids, scores in results:
+            for tlwh, track_id, score in zip(tlwhs, track_ids, scores):
+                if track_id < 0:
+                    continue
+                x1, y1, w, h = tlwh
+                line = save_format.format(frame=frame_id, id=track_id, x1=round(x1, 1), y1=round(y1, 1), w=round(w, 1),
+                                          h=round(h, 1), s=round(score, 2))
+                f.write(line)
+    logger.info('save results to {}'.format(filename))
+
+
+def get_color(idx):
+    idx = (idx + 1) * 50
+    color = ((37 * idx) % 255, (17 * idx) % 255, (29 * idx) % 255)
+
+    return color
+
+
+def write_results_no_score(filename, results):
+    save_format = '{frame},{id},{x1},{y1},{w},{h},-1,-1,-1,-1\n'
+    directory = os.path.dirname(filename)  # Extract the directory path from the file path
+    if not os.path.exists(directory):  # Check if the directory exists
+        os.makedirs(directory)  # Create the directory if it doesn't exist
+    with open(filename, 'w') as f:
+        for frame_id, tlwhs, track_ids in results:
+            for tlwh, track_id in zip(tlwhs, track_ids):
+                if track_id < 0:
+                    continue
+                x1, y1, w, h = tlwh
+                line = save_format.format(frame=frame_id, id=track_id, x1=round(x1, 1), y1=round(y1, 1), w=round(w, 1),
+                                          h=round(h, 1))
+                f.write(line)
+    logger.info('save results to {}'.format(filename))
+
+
+def mot16(root):
+    seqs_train = ['MOT16-02', 'MOT16-04', 'MOT16-05', 'MOT16-09', 'MOT16-10', 'MOT16-11', 'MOT16-13']
+    seqs_test = ['MOT16-01', 'MOT16-03', 'MOT16-06', 'MOT16-07', 'MOT16-08', 'MOT16-12', 'MOT16-14']
+    train_dir = root + '/MOT16/train'
+    test_dir = root + '/MOT16/test'
+    return train_dir, test_dir, seqs_train, seqs_test
+
+
+def mot17(root):
+    seqs_train = ['MOT17-02-DPM', 'MOT17-02-FRCNN', 'MOT17-02-SDP', 'MOT17-04-DPM', 'MOT17-04-FRCNN', 'MOT17-04-SDP',
+                  'MOT17-05-DPM', 'MOT17-05-FRCNN', 'MOT17-05-SDP', 'MOT17-09-DPM', 'MOT17-09-FRCNN', 'MOT17-09-SDP',
+                  'MOT17-10-DPM', 'MOT17-10-FRCNN', 'MOT17-10-SDP', 'MOT17-11-DPM', 'MOT17-11-FRCNN', 'MOT17-11-SDP',
+                  'MOT17-13-DPM', 'MOT17-13-FRCNN', 'MOT17-13-SDP']
+    seqs_test = ['MOT17-01-DPM', 'MOT17-01-FRCNN', 'MOT17-01-SDP', 'MOT17-03-DPM', 'MOT17-03-FRCNN', 'MOT17-03-SDP',
+                 'MOT17-06-DPM', 'MOT17-06-FRCNN', 'MOT17-06-SDP', 'MOT17-07-DPM', 'MOT17-07-FRCNN', 'MOT17-07-SDP',
+                 'MOT17-08-DPM', 'MOT17-08-FRCNN', 'MOT17-08-SDP', 'MOT17-12-DPM', 'MOT17-12-FRCNN', 'MOT17-12-SDP',
+                 'MOT17-14-DPM', 'MOT17-14-FRCNN', 'MOT17-14-SDP']
+    train_dir = root + '/MOT17/train'
+    test_dir = root + '/MOT17/test'
+    return train_dir, test_dir, seqs_train, seqs_test
+
+
+def dancetrack(root):
+    val_numbers = [4, 5, 7, 10, 14, 18, 19, 25, 26, 30, 34, 35, 41, 43, 47, 58, 63, 65, 73, 77, 79, 81, 90, 94, 97]
+    train_numbers = [1, 2, 6, 8, 12, 15, 16, 20, 23, 24, 27, 29, 32, 33, 37, 39, 44, 45, 49, 51, 52, 53, 55, 57, 61, 62,
+                     66, 68, 69, 72, 74, 75, 80, 82, 83, 86, 87, 96, 98, 99]
+    test_numbers = [3, 9, 11, 13, 17, 21, 22, 28, 31, 36, 38, 40, 42, 46, 48, 50, 54, 56, 59, 60, 64, 67, 70, 71, 76,
+                    78, 84, 85, 88, 89, 91, 92, 93, 95, 100]
+    seqs_train = [f"dancetrack{num:04d}" for num in train_numbers]
+    seqs_val = [f"dancetrack{num:04d}" for num in val_numbers]
+    seqs_test = [f"dancetrack{num:04d}" for num in test_numbers]
+    train_dir = root + '/DanceTrack/train/'
+    val_dir = root + '/DanceTrack/val/'
+    test_dir = root + '/DanceTrack/test/'
+    return train_dir, val_dir, test_dir, seqs_train, seqs_val, seqs_test
+
+
+def mot20(root):
+    seqs_train = ['MOT20-01', 'MOT20-02', 'MOT20-03', 'MOT20-05']
+    seqs_test = ['MOT20-04', 'MOT20-06', 'MOT20-07', 'MOT20-08']
+    train_dir = root + '/MOT20/train'
+    test_dir = root + '/MOT20/test'
+    return train_dir, test_dir, seqs_train, seqs_test
+
+
+def mot17_evaluate(data_root, result_dir):
+    train_dir, test_dir, seqs_train, seqs_test = mot17(data_root)
+    seqs = ["02", "04", "05", "09", "10", "11", "13"]  # , "01", "03", "06", "07", "08", "12", "14"]
+    sub_seqs = ["DPM", "SDP", "FRCNN"]
+    for seq in seqs:
+        input_file = result_dir + "/MOT16-" + seq + ".txt"
+        for sub_seq in sub_seqs:
+            output_file = result_dir + "/MOT17-" + seq + "-" + sub_seq + ".txt"
+            with open(input_file) as f:
+                with open(output_file, "w") as f1:
+                    for line in f:
+                        f1.write(line)
+    # evaluate_motmetrics(train_dir, result_dir, seqs_train)
+    evaluate_trackeval(seqs_train, train_dir, result_dir)
+
+
+def evaluate_motmetrics(train_dir, result_dir, seqs_train):
+    accs = []
+    for seq in seqs_train:
+        # eval
+        logger.info('Evaluate seq: {}'.format(seq))
+        evaluator = Evaluator(train_dir, seq, 'mot')
+        accs.append(evaluator.eval_file(os.path.join(result_dir, seq + '.txt')))
+
+    # get summary
+    metrics = mm.metrics.motchallenge_metrics
+    mh = mm.metrics.create()
+    summary = Evaluator.get_summary(accs, seqs_train, metrics)
+    strsummary = mm.io.render_summary(
+        summary,
+        formatters=mh.formatters,
+        namemap=mm.io.motchallenge_metric_names
+    )
+    print(strsummary)
+    Evaluator.save_summary(summary, os.path.join(result_dir, 'summary_{}.xlsx'.format(seqs_train[0].split('-')[0])))
+    with open(os.path.join(result_dir, 'summary_{}.txt'.format(seqs_train[0].split('-')[0])), 'w') as f:
+        f.write(strsummary)
+
+
+def evaluate_trackeval(seqs, gt_folder, trackers_folder):
+    output_folder = './results/'
+    # List of sequences to evaluate
+    sequences = {seq: None for seq in seqs}
+    # sequences = {
+    #     'MOT16-02': None,
+    #     'MOT16-04': None,
+    #     'MOT16-05': None,
+    #     'MOT16-09': None,
+    #     'MOT16-10': None,
+    #     'MOT16-11': None,
+    #     'MOT16-13': None
+    # }
+
+    # Configuration for the evaluation
+    eval_config = {
+        'USE_PARALLEL': False,
+        'NUM_PARALLEL_CORES': 1,
+        'TRACKERS_TO_EVAL': [''],  # List of trackers to evaluate
+        'DATASETS_TO_EVAL': ['mot_challenge'],  # List of datasets to evaluate
+        'BENCHMARK': 'MOT16',  # The benchmark to use (e.g., 'MOT17', 'MOT20')
+        # 'SPLIT_TO_EVAL': 'train',  # Which split to evaluate ('train', 'test')
+        'SKIP_SPLIT_FOL': True,
+        'METRICS': ['CLEAR', 'HOTA', 'Identity'],  # Metrics to evaluate
+        'OUTPUT_FOLDER': output_folder,
+        'TRACKERS_FOLDER': trackers_folder,
+        'GT_FOLDER': gt_folder,
+        'PRINT_CONFIG': False,  # Disable printing of the configuration
+        'TRACKER_SUB_FOLDER': '',
+        'OUTPUT_SUB_FOLDER': '',
+        'SEQ_INFO': sequences
+    }
+
+    # Create an Evaluator
+    evaluator = trackeval.Evaluator(eval_config)
+
+    # Load datasets
+    dataset_list = []
+    for dataset in eval_config['DATASETS_TO_EVAL']:
+        if dataset == 'mot_challenge':
+            dataset_list.append(trackeval.datasets.MotChallenge2DBox(eval_config))
+        else:
+            raise ValueError(f"Dataset {dataset} is not supported in this example.")
+
+    # Load metrics
+    metrics_list = [trackeval.metrics.HOTA(eval_config), trackeval.metrics.CLEAR(eval_config),
+                    trackeval.metrics.Identity(eval_config)]
+
+    sys.stdout = open(os.devnull, 'w')  # Suppress print output
+    # Run evaluation
+    output_res, _ = evaluator.evaluate(dataset_list, metrics_list)
+    sys.stdout = sys.__stdout__  # Restore stdout
+    com_hota = np.average(output_res['MotChallenge2DBox']['']['COMBINED_SEQ']['pedestrian']['HOTA']['HOTA'])
+    com_mota = output_res['MotChallenge2DBox']['']['COMBINED_SEQ']['pedestrian']['CLEAR']['MOTA']
+    com_idf1 = output_res['MotChallenge2DBox']['']['COMBINED_SEQ']['pedestrian']['Identity']['IDF1']
+    idsw = output_res['MotChallenge2DBox']['']['COMBINED_SEQ']['pedestrian']['CLEAR']['IDSW']
+    print(trackers_folder, f"HOTA {com_hota} IDF1 {com_idf1} MOTA {com_mota} IDSW {idsw}")
+
+
+class MOTEvaluator:
+    def __init__(self, args):
+        self.args = args
+        self.show_image = args.show_image
+
+    def evaluate_BYTETrack_singclass(self, class_num, dets, img_files):
+        tracker = BYTETracker(self.args)
+        print("Starting tracking class num: ", class_num)
+        results = []
+        n_frames = int(np.amax(dets[:, 0]))
+        total_time = 0
+        for frame_id in range(n_frames):
+            img0 = cv2.imread(img_files[frame_id])
+            frame_bboxes = dets[dets[:, 0] == frame_id, :][:, 1:]
+            start = time.time()
+            online_targets = tracker.update(frame_bboxes, img0)
+            total_time += time.time() - start
+            online_tlwhs = []
+            online_ids = []
+            for t in online_targets:
+                tid, tlwh = int(t[0]), t[1:]
+                online_tlwhs.append(tlwh)
+                online_ids.append(tid)
+            results.append((frame_id + 1, class_num, online_tlwhs, online_ids))
+        print("BYTETrack FPS: ", round(1.0 / (total_time / n_frames), 2))
+        return results
+
+    def evaluate_trackers(self, args, dets_path, tracker_name="SORT"):
+        ##########
+        train_dir, test_dir, seqs_train, seqs_test = mot16(self.args.data_dir)
+        for video_name in seqs_train:
+            ##################################################################################################
+            if tracker_name == "SORT":
+                from trackers.sort.sort import Sort
+                tracker = Sort(det_thresh=self.args.track_thresh)
+            elif tracker_name == "FairMOT":
+                from trackers.fairmot.multitracker import JDETracker
+                tracker = JDETracker(self.args)
+            elif tracker_name == "MOTDT":
+                from trackers.motdt.motdt_tracker import OnlineTracker
+                tracker = OnlineTracker(min_cls_score=self.args.track_thresh)
+            elif tracker_name == "DeepOCSort":
+                from trackers.integrated_ocsort_embedding.ocsort import OCSort
+                tracker = OCSort(det_thresh=self.args.track_thresh)
+            elif tracker_name == "OCSort":
+                from trackers.ocsort.ocsort import OCSort
+                tracker = OCSort(det_thresh=args.track_thresh, iou_threshold=args.iou_thresh, asso_func=args.asso,
+                                 delta_t=args.deltat, inertia=args.inertia, use_byte=args.use_byte,
+                                 use_gmc=args.use_gmc)
+            elif tracker_name == "DeepSort":
+                from trackers.deepsort.deepsort import DeepSort
+                tracker = DeepSort(min_confidence=self.args.track_thresh)
+            elif tracker_name == "BYTETrack":
+                ori_thresh = self.args.track_thresh
+                if video_name == 'MOT16-05' or video_name == 'MOT16-06':
+                    self.args.track_buffer = 14
+                elif video_name == 'MOT16-13' or video_name == 'MOT16-14':
+                    self.args.track_buffer = 25
+                else:
+                    self.args.track_buffer = 30
+                if video_name == 'MOT16-01':
+                    self.args.track_thresh = 0.65
+                elif video_name == 'MOT16-06':
+                    self.args.track_thresh = 0.65
+                elif video_name == 'MOT16-12':
+                    self.args.track_thresh = 0.7
+                elif video_name == 'MOT16-14':
+                    self.args.track_thresh = 0.67
+                elif video_name in ['MOT20-06', 'MOT20-08']:
+                    self.args.track_thresh = 0.3
+                else:
+                    self.args.track_thresh = ori_thresh
+                tracker = BYTETracker(self.args)
+            elif tracker_name == "LMB":
+                from trackers.joint_lmb.joint_lmb import LMB
+                tracker = LMB(track_thresh=self.args.track_thresh, use_feat=True)
+            else:
+                raise ValueError(f"Unknown tracker: {tracker_name}")
+            ##################################################################################################
+            print("Starting tracking sequence", video_name)
+            results = []
+            npz_lines = np.load(dets_path + "/" + video_name + ".npz")
+            n_frames = int(len(npz_lines.files) / 2)
+            img_path = os.path.join(train_dir, video_name)
+            files = sorted(glob.glob(osp.join(img_path, 'img1') + '/*.jpg'))
+            for frame_id in range(n_frames):
+                img0 = cv2.imread(files[frame_id])
+                # obtain detection for each frame
+                try:
+                    bboxs, reidfeat = npz_lines[str(frame_id) + '_det'], npz_lines[str(frame_id) + '_feat']
+                except:
+                    bboxs, reidfeat = np.empty((0, 4)), np.empty((0, 128))  # no detection
+                dets = np.column_stack((bboxs, reidfeat))
+                # run tracking
+                online_targets = tracker.update(dets, img0)
+                online_tlwhs = []
+                online_ids = []
+                online_scores = []
+                for t in online_targets:
+                    tlwh = t.tlwh
+                    tid = int(t.track_id)
+                    vertical = tlwh[2] / tlwh[3] > 1.6
+                    if tlwh[2] * tlwh[3] > self.args.min_box_area and not vertical:
+                        online_tlwhs.append(tlwh)
+                        online_ids.append(tid)
+                        online_scores.append(t.score)
+                        if self.show_image:
+                            l, t = int(tlwh[0]), int(tlwh[1])
+                            r, b = int(tlwh[0] + tlwh[2]), int(tlwh[1] + tlwh[3])
+                            # draw bbox
+                            color = get_color(tid)
+                            img0 = cv2.circle(img0, (l, t), radius=8, color=color, thickness=-1)
+                            img0 = cv2.rectangle(img0, (l, t), (r, b), color=color, thickness=2)
+                            img0 = cv2.putText(img0, str(tid), org=(l, t), fontFace=cv2.FONT_HERSHEY_SIMPLEX,
+                                               fontScale=0.65, color=(0, 255, 255), thickness=2)
+                # save results
+                results.append((frame_id + 1, online_tlwhs, online_ids))
+                if self.show_image:
+                    str_show = 'Frame {}'.format(frame_id)
+                    img0 = cv2.putText(img0, str_show, org=(img0.shape[1] - 400, 30), fontFace=cv2.FONT_HERSHEY_SIMPLEX,
+                                       fontScale=1, color=(255, 255, 255), thickness=2)
+                    scale_percent = 0.6  # percent of original size
+                    dim = (int(img0.shape[1] * scale_percent), int(img0.shape[0] * scale_percent))
+                    resized = cv2.resize(img0, dim, interpolation=cv2.INTER_AREA)  # resize image
+                    cv2.imshow('Image', resized)
+                    cv2.moveWindow('Image', 200, 200)
+                    cv2.waitKey(1)
+                if frame_id == n_frames - 1:
+                    result_filename = os.path.join(self.args.result_dir, '{}.txt'.format(video_name))
+                    write_results_no_score(result_filename, results)
+        # MOT16 Evaluation
+        # evaluate_motmetrics(train_dir, self.args.result_dir, seqs_train)
+        evaluate_trackeval(seqs_train, train_dir, self.args.result_dir)
+        # MOT17 Evaluation
+        mot17_evaluate(self.args.data_dir, self.args.result_dir)
+    ### END
+
+
+def get_color(idx):
+    idx = (idx + 1) * 50
+    color = ((37 * idx) % 255, (17 * idx) % 255, (29 * idx) % 255)
+
+    return color
+
+
+def vdemo_from_rfile(rfile, img_folder):
+    tracks = np.loadtxt(rfile, delimiter=",")
+    # '{frame},{id},{top},{left},{w},{h},-1,-1,-1,-1\n'
+    files = sorted(glob.glob(img_folder + '/*.jpg'))
+    n_frames = len(files)
+    video_name = os.path.join(os.path.dirname(rfile), os.path.basename(rfile).split(".")[0] + ".mp4")
+    size = cv2.imread(files[0]).shape[0:2][::-1]
+    out = cv2.VideoWriter(video_name, cv2.VideoWriter_fourcc(*'mp4v'), 30, size)
+    for frame_id in range(n_frames):
+        img0 = cv2.imread(files[frame_id])
+        frame_tracks = tracks[tracks[:, 0] == frame_id + 1]
+        for tt in frame_tracks:
+            tlwh = tt[2:6]
+            tid = int(tt[1])
+            l, t = int(tlwh[0]), int(tlwh[1])
+            r, b = int(tlwh[0] + tlwh[2]), int(tlwh[1] + tlwh[3])
+            # cxy = (int(tlwh[0] + tlwh[2] / 2), int(tlwh[1] + tlwh[3] / 2))
+            # draw bbox
+            color = get_color(tid)
+            # img0 = cv2.circle(img0, cxy, radius=8, color=color, thickness=-1)
+            img0 = cv2.rectangle(img0, (l, t), (r, b), color=color, thickness=2)
+            img0 = cv2.putText(img0, str(tid), org=(l, t + 15), fontFace=cv2.FONT_HERSHEY_SIMPLEX, fontScale=0.65,
+                               color=color, thickness=2)
+        cv2.imshow(rfile, img0)
+        cv2.waitKey(1)
+        out.write(img0)
+    out.release()
+
+
+if __name__ == "__main__":
+    mot17_evaluate("/media/ubuntu/2715608D71CBF6FC/datasets/mot", "./results/detector_cstrack/BYTETrack/")
+    # seq = "MOT16-02"
+    # vdemo_from_rfile(f"results/bytetrack/bytetrack/{seq}.txt",
+    #                  f"/media/ubuntu/2715608D71CBF6FC/datasets/mot/MOT16/train/{seq}/img1/")
diff --git a/reid_evaluation.py b/reid_evaluation.py
new file mode 100644
index 0000000000000000000000000000000000000000..697f86d997883b03719b222a35fd19685ba31ef3
--- /dev/null
+++ b/reid_evaluation.py
@@ -0,0 +1,97 @@
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+from sklearn.metrics.pairwise import cosine_similarity
+
+
+def compute_average_similarity(detectors, seqs, conf=0.5):
+    for idx, detector in enumerate(detectors):
+        for seq in seqs:
+            det = np.load(f"./dets/{detector}/{seq}.npz")
+            nframes = int(len(det.files) / 2)
+            fidx = 0
+            seq_mean = 0
+            seq_var = 0
+            for frame in range(nframes):
+                bbox = det[f'{frame}_det']
+                reid_vectors = det[f'{frame}_feat'][bbox[:, 4] > conf]
+                if reid_vectors.shape[0] <= 1:
+                    continue
+                similarity_matrix = cosine_similarity(reid_vectors)
+                # Extract upper triangle of similarity matrix (excluding diagonal)
+                upper_tri = similarity_matrix[np.triu_indices(len(reid_vectors), k=1)]
+                seq_mean += np.mean(upper_tri)  # Mean pairwise similarity
+                seq_var += np.std(upper_tri)  # Variance of similarity scores
+                fidx += 1
+            seq_mean /= fidx
+            seq_var /= fidx
+            print(detector, seq, seq_mean, seq_var)
+
+
+def visual_similarity(frame=100, conf=0.3):
+    # Create a 4x4 grid of subplots
+    fig, axes = plt.subplots(3, 4, figsize=(12, 7))  # Adjust figsize for clarity
+    axes = axes.flatten()  # Flatten the 2D array of axes for easy iteration
+
+    # Iterate over detectors and populate the heatmaps
+    detectors = ['detector_poi', 'detector_trades', 'detectors_yolov11', 'detector_jde',
+                 'detector_cstrack', 'detector_fairmot128', 'detector_gsdt', 'detector_bytetrack']
+    detector_names = ['POI', 'TraDes', 'YOLOv11_SBS50', 'JDE', 'CSTrack', 'FairMOT', 'GSDT', 'YOLOX_SBS50']
+    seq = "MOT16-04"
+    for idx, detector in enumerate(detectors):
+        det = np.load(f"./dets/{detector}/{seq}.npz")
+        # Step 1: Example ReID vectors (replace with your actual data for each detector)
+        bbox = det[f'{frame}_det']
+        reid_vectors = det[f'{frame}_feat'][bbox[:, 4] > conf]
+        # Step 2: Compute the similarity matrix
+        similarity_matrix = cosine_similarity(reid_vectors)
+        # Step 3: Visualize the heatmap in the corresponding subplot
+        sns.heatmap(similarity_matrix, annot=False, cmap="YlGnBu", vmin=0, vmax=1, ax=axes[idx])
+        axes[idx].set_title(f"{seq}, {detector_names[idx]}")
+        # axes[idx].set_xlabel("Vector Index")
+        # axes[idx].set_ylabel("Vector Index")
+        # Step 4: Set discrete ticks (e.g., every 2nd index)
+        tick_indices = np.arange(0, len(reid_vectors), 2)  # Show every 2nd index (0, 2, 4, 6, 8)
+        axes[idx].set_xticks(tick_indices)
+        axes[idx].set_yticks(tick_indices)
+
+    detectors_mot20 = ['detector_cstrack', 'detector_fairmot128', 'detector_gsdt', 'detector_bytetrack']
+    detectors_mot20_names = ['CSTrack', 'FairMOT', 'GSDT', 'YOLOX_SBS50']
+    seq = "MOT20-05"
+    for idx, detector in enumerate(detectors_mot20):
+        det = np.load(f"./dets/{detector}/{seq}.npz")
+        # Step 1: Example ReID vectors (replace with your actual data for each detector)
+        bbox = det[f'{frame}_det']
+        reid_vectors = det[f'{frame}_feat'][bbox[:, 4] > conf]
+        # Step 2: Compute the similarity matrix
+        similarity_matrix = cosine_similarity(reid_vectors)
+        # Step 3: Visualize the heatmap in the corresponding subplot
+        sns.heatmap(similarity_matrix, annot=False, cmap="YlGnBu", vmin=0, vmax=1, ax=axes[idx + len(detectors)])
+        axes[idx + len(detectors)].set_title(f"{seq}, {detectors_mot20_names[idx]}")
+        # axes[idx].set_xlabel("Vector Index")
+        # axes[idx].set_ylabel("Vector Index")
+        # Step 4: Set discrete ticks (e.g., every 2nd index)
+        tick_indices = np.arange(0, len(reid_vectors), 2)  # Show every 2nd index (0, 2, 4, 6, 8)
+        axes[idx + len(detectors)].set_xticks(tick_indices)
+        axes[idx + len(detectors)].set_yticks(tick_indices)
+    # Hide any unused subplots (if fewer than 16 detectors)
+    for idx in range(len(detectors) + len(detectors_mot20), len(axes)):
+        axes[idx].axis('off')
+    # Adjust layout to prevent overlap
+    # plt.subplots_adjust(hspace=5.5)  # Default is ~0.2; increase for wider spacing
+    plt.tight_layout(h_pad=1.5, w_pad=2.0, rect=[0, 0, 1, 0.97])
+    # Save the figure as a PDF file
+    plt.savefig("reid_similarity_heatmaps.pdf", format="pdf", bbox_inches="tight")
+    plt.show()
+
+
+if __name__ == "__main__":
+    visual_similarity()
+
+    detectors = ['detector_poi', 'detector_trades', 'detectors_yolov11', 'detector_jde',
+                 'detector_cstrack', 'detector_fairmot128', 'detector_gsdt', 'detector_bytetrack']
+    seqs = ['MOT16-02', 'MOT16-04', 'MOT16-05', 'MOT16-09', 'MOT16-10', 'MOT16-11', 'MOT16-13']
+    detectors_mot20 = ['detector_cstrack', 'detector_fairmot128', 'detector_gsdt', 'detector_bytetrack']
+    seqs_mot20 = ['MOT20-01', 'MOT20-02', 'MOT20-03', 'MOT20-05']
+    compute_average_similarity(detectors, seqs)
+    compute_average_similarity(detectors_mot20, seqs_mot20)
diff --git a/track.py b/track.py
new file mode 100644
index 0000000000000000000000000000000000000000..5e5b0f34a17a598af6be2d5fa56d8a16b2cba5ff
--- /dev/null
+++ b/track.py
@@ -0,0 +1,37 @@
+import argparse
+from mot_evaluator import MOTEvaluator
+
+
+def make_parser():
+    parser = argparse.ArgumentParser("Object State Eval")
+    parser.add_argument("--data_dir", default="/media/ubuntu/2715608D71CBF6FC/datasets/mot", type=str, help="eval seed")
+    parser.add_argument("--result_dir", default="./results/bytetrack", type=str, help="eval seed")
+    parser.add_argument("--show_image", default=False, type=bool, help="eval seed")
+    # tracking args
+    parser.add_argument("--track_thresh", type=float, default=0.3, help="detection confidence threshold")
+    parser.add_argument("--track_buffer", type=int, default=30, help="the frames for keep lost tracks")
+    parser.add_argument("--match_thresh", type=float, default=0.7, help="matching threshold for tracking")
+    parser.add_argument("--min-box-area", type=float, default=100, help='filter out tiny boxes')
+    parser.add_argument("--mot20", dest="mot20", default=False, action="store_true", help="test mot20.")
+    # tracking args OCSORT
+    parser.add_argument("--iou_thresh", type=float, default=0.3, help="the iou threshold in Sort for matching")
+    parser.add_argument('--asso', default="iou", help="similarity function: iou/giou/diou/ciou/ctdis")
+    parser.add_argument("--deltat", type=int, default=3, help="time step difference to estimate direction")
+    parser.add_argument("--inertia", type=float, default=0.2, help="the weight of VDC term in cost matrix")
+    parser.add_argument("--use_byte", type=bool, default=True, help="use BYTE association")
+    # add cmc for fixing the camera motion
+    parser.add_argument("--use_gmc", default=True, type=bool, help="use Camera Motion Compensation")
+
+    return parser
+
+
+if __name__ == "__main__":
+    args = make_parser().parse_args()
+    evaluator = MOTEvaluator(args)
+    for detector in ['detector_poi', 'detector_trades', 'detector_gsdt', 'detector_jde', 'detector_cstrack',
+                     'detector_fairmot128', 'detector_bytetrack', 'detectors_yolov11']:
+        for tracker in ['SORT', 'BYTETrack', 'OCSort', 'DeepSort', 'MOTDT', 'FairMOT', 'DeepOCSort', 'LMB']:
+            print(f"#################### {detector} #################### {tracker} ####################")
+            args.result_dir = f"./results/{detector}/{tracker}"
+            evaluator.evaluate_trackers(args, f"./dets/{detector}", tracker)
+    ###############
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diff --git a/trackers/bytetrack/basetrack.py b/trackers/bytetrack/basetrack.py
new file mode 100644
index 0000000000000000000000000000000000000000..1d77bb4d3967876316244c5d24a5767ad88898aa
--- /dev/null
+++ b/trackers/bytetrack/basetrack.py
@@ -0,0 +1,56 @@
+import numpy as np
+from collections import OrderedDict
+
+
+class TrackState(object):
+    New = 0
+    Tracked = 1
+    Lost = 2
+    Removed = 3
+
+
+class BaseTrack(object):
+    _count = 0
+
+    track_id = 0
+    is_activated = False
+    state = TrackState.New
+
+    history = OrderedDict()
+    features = []
+    curr_feature = None
+    score = 0
+    start_frame = 0
+    frame_id = 0
+    time_since_update = 0
+
+    # multi-camera
+    location = (np.inf, np.inf)
+
+    @property
+    def end_frame(self):
+        return self.frame_id
+
+    @staticmethod
+    def next_id():
+        BaseTrack._count += 1
+        return BaseTrack._count
+
+    @staticmethod
+    def init_id():
+        BaseTrack._count = 0
+
+    def activate(self, *args):
+        raise NotImplementedError
+
+    def predict(self):
+        raise NotImplementedError
+
+    def update(self, *args, **kwargs):
+        raise NotImplementedError
+
+    def mark_lost(self):
+        self.state = TrackState.Lost
+
+    def mark_removed(self):
+        self.state = TrackState.Removed
diff --git a/trackers/bytetrack/byte_tracker.py b/trackers/bytetrack/byte_tracker.py
new file mode 100644
index 0000000000000000000000000000000000000000..bf1ba9a532e95481771c351e13dda0b0d1eae755
--- /dev/null
+++ b/trackers/bytetrack/byte_tracker.py
@@ -0,0 +1,366 @@
+import numpy as np
+
+from .kalman_filter import KalmanFilter
+from . import matching
+from .basetrack import BaseTrack, TrackState
+from .cmc import GMC
+
+
+class STrack(BaseTrack):
+    shared_kalman = KalmanFilter()
+
+    def __init__(self, tlwh, score):
+
+        # wait activate
+        self._tlwh = np.asarray(tlwh, dtype=float)
+        self.kalman_filter = None
+        self.mean, self.covariance = None, None
+        self.is_activated = False
+
+        self.score = score
+        self.tracklet_len = 0
+
+    def predict(self):
+        mean_state = self.mean.copy()
+        if self.state != TrackState.Tracked:
+            mean_state[7] = 0
+        self.mean, self.covariance = self.kalman_filter.predict(mean_state, self.covariance)
+
+    @staticmethod
+    def multi_predict(stracks, H):
+        if len(stracks) > 0:
+            multi_mean = np.asarray([st.mean.copy() for st in stracks])
+            multi_covariance = np.asarray([st.covariance for st in stracks])
+            for i, st in enumerate(stracks):
+                if st.state != TrackState.Tracked:
+                    multi_mean[i][7] = 0
+            multi_mean, multi_covariance = STrack.shared_kalman.multi_predict(multi_mean, multi_covariance)
+            for i, (mean, cov) in enumerate(zip(multi_mean, multi_covariance)):
+                if H is not None:
+                    # Apply Camera Motion Compensation using the transformation matrix J
+                    # J = np.kron(np.eye(4, dtype=float), H[:2, :2])
+                    # tx, ty = H[0, 2], H[1, 2]
+                    a11, a12, tx = H[0]
+                    a21, a22, ty = H[1]
+                    J = np.array([
+                        [a11, a12, 0, 0, 0, 0, 0, 0],  # x
+                        [a21, a22, 0, 0, 0, 0, 0, 0],  # y
+                        [0, 0, np.sqrt(a11 ** 2 + a21 ** 2), 0, 0, 0, 0, 0],  # w
+                        [0, 0, 0, np.sqrt(a12 ** 2 + a22 ** 2), 0, 0, 0, 0],  # h
+                        [0, 0, 0, 0, a11, a12, 0, 0],  # dx
+                        [0, 0, 0, 0, a21, a22, 0, 0],  # dy
+                        [0, 0, 0, 0, 0, 0, np.sqrt(a11 ** 2 + a21 ** 2), 0],  # dw
+                        [0, 0, 0, 0, 0, 0, 0, np.sqrt(a12 ** 2 + a22 ** 2)]  # dh
+                    ])
+                    mean = np.dot(J, mean) + np.array([tx, ty, 0, 0, 0, 0, 0, 0])  # -state
+                    cov = J @ cov @ J.T
+                    #####
+                stracks[i].mean = mean
+                stracks[i].covariance = cov
+
+    def activate(self, kalman_filter, frame_id):
+        """Start a new tracklet"""
+        self.kalman_filter = kalman_filter
+        self.track_id = self.next_id()
+        self.mean, self.covariance = self.kalman_filter.initiate(self.tlwh_to_xyah(self._tlwh))
+
+        self.tracklet_len = 0
+        self.state = TrackState.Tracked
+        if frame_id == 1:
+            self.is_activated = True
+        # self.is_activated = True
+        self.frame_id = frame_id
+        self.start_frame = frame_id
+
+    def re_activate(self, new_track, frame_id, new_id=False):
+        self.mean, self.covariance = self.kalman_filter.update(
+            self.mean, self.covariance, self.tlwh_to_xyah(new_track.tlwh)
+        )
+        self.tracklet_len = 0
+        self.state = TrackState.Tracked
+        self.is_activated = True
+        self.frame_id = frame_id
+        if new_id:
+            self.track_id = self.next_id()
+        self.score = new_track.score
+
+    def update(self, new_track, frame_id):
+        """
+        Update a matched track
+        :type new_track: STrack
+        :type frame_id: int
+        :type update_feature: bool
+        :return:
+        """
+        self.frame_id = frame_id
+        self.tracklet_len += 1
+
+        new_tlwh = new_track.tlwh
+        self.mean, self.covariance = self.kalman_filter.update(
+            self.mean, self.covariance, self.tlwh_to_xyah(new_tlwh))
+        self.state = TrackState.Tracked
+        self.is_activated = True
+
+        self.score = new_track.score
+
+    @property
+    # @jit(nopython=True)
+    def tlwh(self):
+        """Get current position in bounding box format `(top left x, top left y,
+                width, height)`.
+        """
+        if self.mean is None:
+            return self._tlwh.copy()
+        ret = self.mean[:4].copy()
+        ret[2] *= ret[3]
+        ret[:2] -= ret[2:] / 2
+        return ret
+
+    @property
+    # @jit(nopython=True)
+    def tlbr(self):
+        """Convert bounding box to format `(min x, min y, max x, max y)`, i.e.,
+        `(top left, bottom right)`.
+        """
+        ret = self.tlwh.copy()
+        ret[2:] += ret[:2]
+        return ret
+
+    @staticmethod
+    # @jit(nopython=True)
+    def tlwh_to_xyah(tlwh):
+        """Convert bounding box to format `(center x, center y, aspect ratio,
+        height)`, where the aspect ratio is `width / height`.
+        """
+        ret = np.asarray(tlwh).copy()
+        ret[:2] += ret[2:] / 2
+        ret[2] /= ret[3]
+        return ret
+
+    def to_xyah(self):
+        return self.tlwh_to_xyah(self.tlwh)
+
+    @staticmethod
+    # @jit(nopython=True)
+    def tlbr_to_tlwh(tlbr):
+        ret = np.asarray(tlbr).copy()
+        ret[2:] -= ret[:2]
+        return ret
+
+    @staticmethod
+    # @jit(nopython=True)
+    def tlwh_to_tlbr(tlwh):
+        ret = np.asarray(tlwh).copy()
+        ret[2:] += ret[:2]
+        return ret
+
+    def __repr__(self):
+        return 'OT_{}_({}-{})'.format(self.track_id, self.start_frame, self.end_frame)
+
+
+class BYTETracker(object):
+    def __init__(self, args, frame_rate=30):
+        self.tracked_stracks = []  # type: list[STrack]
+        self.lost_stracks = []  # type: list[STrack]
+        self.removed_stracks = []  # type: list[STrack]
+
+        self.frame_id = 0
+        STrack.init_id()
+        self.args = args
+        # self.det_thresh = args.track_thresh
+        self.det_thresh = args.track_thresh + 0.1
+        self.buffer_size = int(frame_rate / 30.0 * args.track_buffer)
+        self.max_time_lost = self.buffer_size
+        self.kalman_filter = KalmanFilter()
+        self.use_gmc = args.use_gmc
+        self.gmc = GMC(method="cmc", verbose=None)
+        self.asso_func = args.asso
+
+    def update(self, output_results, image):
+        self.frame_id += 1
+        activated_starcks = []
+        refind_stracks = []
+        lost_stracks = []
+        removed_stracks = []
+
+        # if output_results.shape[1] == 5:
+        #     scores = output_results[:, 4]
+        #     bboxes = output_results[:, :4]
+        # else:
+        #     output_results = output_results.cpu().numpy()
+        #     scores = output_results[:, 4] * output_results[:, 5]
+        #     bboxes = output_results[:, :4]  # x1y1x2y2
+        # img_h, img_w = img_info[0], img_info[1]
+        # scale = min(img_size[0] / float(img_h), img_size[1] / float(img_w))
+        # bboxes /= scale
+
+        scores = output_results[:, 4]
+        bboxes = output_results[:, :4]
+
+        if len(scores) > 1:
+            threshold = scores[np.argmin(np.diff(scores))]
+            if threshold < self.det_thresh:
+                threshold = self.det_thresh
+        else:
+            threshold = self.det_thresh
+        remain_inds = scores >= threshold
+        inds_low = scores > 0.1
+        inds_high = scores <= threshold
+
+        # remain_inds = scores > self.args.track_thresh
+        # inds_low = scores > 0.1
+        # inds_high = scores < self.args.track_thresh
+
+        inds_second = np.logical_and(inds_low, inds_high)
+        dets_second = bboxes[inds_second]
+        dets = bboxes[remain_inds]
+        scores_keep = scores[remain_inds]
+        scores_second = scores[inds_second]
+
+        if len(dets) > 0:
+            '''Detections'''
+            detections = [STrack(STrack.tlbr_to_tlwh(tlbr), s) for
+                          (tlbr, s) in zip(dets, scores_keep)]
+        else:
+            detections = []
+
+        ''' Add newly detected tracklets to tracked_stracks'''
+        unconfirmed = []
+        tracked_stracks = []  # type: list[STrack]
+        for track in self.tracked_stracks:
+            if not track.is_activated:
+                unconfirmed.append(track)
+            else:
+                tracked_stracks.append(track)
+
+        ''' Step 2: First association, with high score detection boxes'''
+        strack_pool = joint_stracks(tracked_stracks, self.lost_stracks)
+        # Predict the current location with KF
+        H = None
+        if self.use_gmc:
+            H = self.gmc.applyCMC(image)
+        STrack.multi_predict(strack_pool, H)
+        dists = matching.iou_distance(strack_pool, detections)
+        if not self.args.mot20:
+            dists = matching.fuse_score(dists, detections)
+        matches, u_track, u_detection = matching.linear_assignment(dists, thresh=self.args.match_thresh)
+
+        for itracked, idet in matches:
+            track = strack_pool[itracked]
+            det = detections[idet]
+            if track.state == TrackState.Tracked:
+                track.update(detections[idet], self.frame_id)
+                activated_starcks.append(track)
+            else:
+                track.re_activate(det, self.frame_id, new_id=False)
+                refind_stracks.append(track)
+
+        ''' Step 3: Second association, with low score detection boxes'''
+        # association the untrack to the low score detections
+        if len(dets_second) > 0:
+            '''Detections'''
+            detections_second = [STrack(STrack.tlbr_to_tlwh(tlbr), s) for
+                                 (tlbr, s) in zip(dets_second, scores_second)]
+        else:
+            detections_second = []
+        r_tracked_stracks = [strack_pool[i] for i in u_track if strack_pool[i].state == TrackState.Tracked]
+        dists = matching.iou_distance(r_tracked_stracks, detections_second)
+        matches, u_track, u_detection_second = matching.linear_assignment(dists, thresh=0.5)
+        for itracked, idet in matches:
+            track = r_tracked_stracks[itracked]
+            det = detections_second[idet]
+            if track.state == TrackState.Tracked:
+                track.update(det, self.frame_id)
+                activated_starcks.append(track)
+            else:
+                track.re_activate(det, self.frame_id, new_id=False)
+                refind_stracks.append(track)
+
+        for it in u_track:
+            track = r_tracked_stracks[it]
+            if not track.state == TrackState.Lost:
+                track.mark_lost()
+                lost_stracks.append(track)
+
+        '''Deal with unconfirmed tracks, usually tracks with only one beginning frame'''
+        detections = [detections[i] for i in u_detection]
+        dists = matching.iou_distance(unconfirmed, detections)
+        if not self.args.mot20:
+            dists = matching.fuse_score(dists, detections)
+        matches, u_unconfirmed, u_detection = matching.linear_assignment(dists, thresh=0.7)
+        for itracked, idet in matches:
+            unconfirmed[itracked].update(detections[idet], self.frame_id)
+            activated_starcks.append(unconfirmed[itracked])
+        for it in u_unconfirmed:
+            track = unconfirmed[it]
+            track.mark_removed()
+            removed_stracks.append(track)
+
+        """ Step 4: Init new stracks"""
+        for inew in u_detection:
+            track = detections[inew]
+            if track.score < self.det_thresh:
+                continue
+            track.activate(self.kalman_filter, self.frame_id)
+            activated_starcks.append(track)
+        """ Step 5: Update state"""
+        for track in self.lost_stracks:
+            if self.frame_id - track.end_frame > self.max_time_lost:
+                track.mark_removed()
+                removed_stracks.append(track)
+
+        # print('Ramained match {} s'.format(t4-t3))
+
+        self.tracked_stracks = [t for t in self.tracked_stracks if t.state == TrackState.Tracked]
+        self.tracked_stracks = joint_stracks(self.tracked_stracks, activated_starcks)
+        self.tracked_stracks = joint_stracks(self.tracked_stracks, refind_stracks)
+        self.lost_stracks = sub_stracks(self.lost_stracks, self.tracked_stracks)
+        self.lost_stracks.extend(lost_stracks)
+        self.lost_stracks = sub_stracks(self.lost_stracks, self.removed_stracks)
+        self.removed_stracks.extend(removed_stracks)
+        self.tracked_stracks, self.lost_stracks = remove_duplicate_stracks(self.tracked_stracks, self.lost_stracks)
+        # get scores of lost tracks
+        output_stracks = [track for track in self.tracked_stracks if track.is_activated]
+
+        return output_stracks
+
+
+def joint_stracks(tlista, tlistb):
+    exists = {}
+    res = []
+    for t in tlista:
+        exists[t.track_id] = 1
+        res.append(t)
+    for t in tlistb:
+        tid = t.track_id
+        if not exists.get(tid, 0):
+            exists[tid] = 1
+            res.append(t)
+    return res
+
+
+def sub_stracks(tlista, tlistb):
+    stracks = {}
+    for t in tlista:
+        stracks[t.track_id] = t
+    for t in tlistb:
+        tid = t.track_id
+        if stracks.get(tid, 0):
+            del stracks[tid]
+    return list(stracks.values())
+
+
+def remove_duplicate_stracks(stracksa, stracksb):
+    pdist = matching.iou_distance(stracksa, stracksb)
+    pairs = np.where(pdist < 0.15)
+    dupa, dupb = list(), list()
+    for p, q in zip(*pairs):
+        timep = stracksa[p].frame_id - stracksa[p].start_frame
+        timeq = stracksb[q].frame_id - stracksb[q].start_frame
+        if timep > timeq:
+            dupb.append(q)
+        else:
+            dupa.append(p)
+    resa = [t for i, t in enumerate(stracksa) if not i in dupa]
+    resb = [t for i, t in enumerate(stracksb) if not i in dupb]
+    return resa, resb
diff --git a/trackers/bytetrack/cmc.py b/trackers/bytetrack/cmc.py
new file mode 100644
index 0000000000000000000000000000000000000000..736fe95887fff01fe6bdb8c3f421b5d5ba738498
--- /dev/null
+++ b/trackers/bytetrack/cmc.py
@@ -0,0 +1,343 @@
+import cv2
+import matplotlib.pyplot as plt
+import numpy as np
+import copy
+import time
+
+
+class GMC:
+    def __init__(self, method='cmc', downscale=2, verbose=None):
+        super(GMC, self).__init__()
+
+        self.method = method
+        self.downscale = max(1, int(downscale))
+
+        if self.method == 'orb':
+            self.detector = cv2.FastFeatureDetector_create(20)
+            self.extractor = cv2.ORB_create()
+            self.matcher = cv2.BFMatcher(cv2.NORM_HAMMING)
+
+        elif self.method == 'sift':
+            self.detector = cv2.SIFT_create(nOctaveLayers=3, contrastThreshold=0.02, edgeThreshold=20)
+            self.extractor = cv2.SIFT_create(nOctaveLayers=3, contrastThreshold=0.02, edgeThreshold=20)
+            self.matcher = cv2.BFMatcher(cv2.NORM_L2)
+
+        elif self.method == 'ecc':
+            number_of_iterations = 5000
+            termination_eps = 1e-6
+            self.warp_mode = cv2.MOTION_EUCLIDEAN
+            self.criteria = (cv2.TERM_CRITERIA_EPS | cv2.TERM_CRITERIA_COUNT, number_of_iterations, termination_eps)
+
+        elif self.method == 'sparseOptFlow':
+            self.feature_params = dict(maxCorners=1000, qualityLevel=0.01, minDistance=1, blockSize=3,
+                                       useHarrisDetector=False, k=0.04)
+            # self.gmc_file = open('GMC_results.txt', 'w')
+
+        elif self.method == 'cmc':
+            self.prev_gray = None
+            # self.gmcFile = open("./GMC-11-2.txt", 'r')
+        elif self.method == 'none' or self.method == 'None':
+            self.method = 'none'
+        else:
+            raise ValueError("Error: Unknown CMC method:" + method)
+
+        self.prevFrame = None
+        self.prevKeyPoints = None
+        self.prevDescriptors = None
+
+        self.initializedFirstFrame = False
+
+    def apply(self, raw_frame, detections=None):
+        if self.method == 'orb' or self.method == 'sift':
+            return self.applyFeaures(raw_frame, detections)
+        elif self.method == 'ecc':
+            return self.applyEcc(raw_frame, detections)
+        elif self.method == 'sparseOptFlow':
+            return self.applySparseOptFlow(raw_frame, detections)
+        elif self.method == 'cmc':
+            return self.applyFile(raw_frame, detections)
+        elif self.method == 'none':
+            return np.eye(2, 3)
+        else:
+            return np.eye(2, 3)
+
+    def applyEcc(self, raw_frame, detections=None):
+
+        # Initialize
+        height, width, _ = raw_frame.shape
+        frame = cv2.cvtColor(raw_frame, cv2.COLOR_BGR2GRAY)
+        H = np.eye(2, 3, dtype=np.float32)
+
+        # Downscale image (TODO: consider using pyramids)
+        if self.downscale > 1.0:
+            frame = cv2.GaussianBlur(frame, (3, 3), 1.5)
+            frame = cv2.resize(frame, (width // self.downscale, height // self.downscale))
+            width = width // self.downscale
+            height = height // self.downscale
+
+        # Handle first frame
+        if not self.initializedFirstFrame:
+            # Initialize data
+            self.prevFrame = frame.copy()
+
+            # Initialization done
+            self.initializedFirstFrame = True
+
+            return H
+
+        # Run the ECC algorithm. The results are stored in warp_matrix.
+        # (cc, H) = cv2.findTransformECC(self.prevFrame, frame, H, self.warp_mode, self.criteria)
+        try:
+            (cc, H) = cv2.findTransformECC(self.prevFrame, frame, H, self.warp_mode, self.criteria, None, 1)
+        except:
+            print('Warning: find transform failed. Set warp as identity')
+
+        return H
+
+    def applyFeaures(self, raw_frame, detections=None):
+
+        # Initialize
+        height, width, _ = raw_frame.shape
+        frame = cv2.cvtColor(raw_frame, cv2.COLOR_BGR2GRAY)
+        H = np.eye(2, 3)
+
+        # Downscale image (TODO: consider using pyramids)
+        if self.downscale > 1.0:
+            # frame = cv2.GaussianBlur(frame, (3, 3), 1.5)
+            frame = cv2.resize(frame, (width // self.downscale, height // self.downscale))
+            width = width // self.downscale
+            height = height // self.downscale
+
+        # find the keypoints
+        mask = np.zeros_like(frame)
+        # mask[int(0.05 * height): int(0.95 * height), int(0.05 * width): int(0.95 * width)] = 255
+        mask[int(0.02 * height): int(0.98 * height), int(0.02 * width): int(0.98 * width)] = 255
+        if detections is not None:
+            for det in detections:
+                tlbr = (det[:4] / self.downscale).astype(np.int_)
+                mask[tlbr[1]:tlbr[3], tlbr[0]:tlbr[2]] = 0
+
+        keypoints = self.detector.detect(frame, mask)
+
+        # compute the descriptors
+        keypoints, descriptors = self.extractor.compute(frame, keypoints)
+
+        # Handle first frame
+        if not self.initializedFirstFrame:
+            # Initialize data
+            self.prevFrame = frame.copy()
+            self.prevKeyPoints = copy.copy(keypoints)
+            self.prevDescriptors = copy.copy(descriptors)
+
+            # Initialization done
+            self.initializedFirstFrame = True
+
+            return H
+
+        # Match descriptors.
+        knnMatches = self.matcher.knnMatch(self.prevDescriptors, descriptors, 2)
+
+        # Filtered matches based on smallest spatial distance
+        matches = []
+        spatialDistances = []
+
+        maxSpatialDistance = 0.25 * np.array([width, height])
+
+        # Handle empty matches case
+        if len(knnMatches) == 0:
+            # Store to next iteration
+            self.prevFrame = frame.copy()
+            self.prevKeyPoints = copy.copy(keypoints)
+            self.prevDescriptors = copy.copy(descriptors)
+
+            return H
+
+        for m, n in knnMatches:
+            if m.distance < 0.9 * n.distance:
+                prevKeyPointLocation = self.prevKeyPoints[m.queryIdx].pt
+                currKeyPointLocation = keypoints[m.trainIdx].pt
+
+                spatialDistance = (prevKeyPointLocation[0] - currKeyPointLocation[0],
+                                   prevKeyPointLocation[1] - currKeyPointLocation[1])
+
+                if (np.abs(spatialDistance[0]) < maxSpatialDistance[0]) and \
+                        (np.abs(spatialDistance[1]) < maxSpatialDistance[1]):
+                    spatialDistances.append(spatialDistance)
+                    matches.append(m)
+
+        meanSpatialDistances = np.mean(spatialDistances, 0)
+        stdSpatialDistances = np.std(spatialDistances, 0)
+
+        inliesrs = (spatialDistances - meanSpatialDistances) < 2.5 * stdSpatialDistances
+
+        goodMatches = []
+        prevPoints = []
+        currPoints = []
+        for i in range(len(matches)):
+            if inliesrs[i, 0] and inliesrs[i, 1]:
+                goodMatches.append(matches[i])
+                prevPoints.append(self.prevKeyPoints[matches[i].queryIdx].pt)
+                currPoints.append(keypoints[matches[i].trainIdx].pt)
+
+        prevPoints = np.array(prevPoints)
+        currPoints = np.array(currPoints)
+
+        # Draw the keypoint matches on the output image
+        if 0:
+            matches_img = np.hstack((self.prevFrame, frame))
+            matches_img = cv2.cvtColor(matches_img, cv2.COLOR_GRAY2BGR)
+            W = np.size(self.prevFrame, 1)
+            for m in goodMatches:
+                prev_pt = np.array(self.prevKeyPoints[m.queryIdx].pt, dtype=np.int_)
+                curr_pt = np.array(keypoints[m.trainIdx].pt, dtype=np.int_)
+                curr_pt[0] += W
+                color = np.random.randint(0, 255, (3,))
+                color = (int(color[0]), int(color[1]), int(color[2]))
+
+                matches_img = cv2.line(matches_img, prev_pt, curr_pt, tuple(color), 1, cv2.LINE_AA)
+                matches_img = cv2.circle(matches_img, prev_pt, 2, tuple(color), -1)
+                matches_img = cv2.circle(matches_img, curr_pt, 2, tuple(color), -1)
+
+            plt.figure()
+            plt.imshow(matches_img)
+            plt.show()
+
+        # Find rigid matrix
+        if (np.size(prevPoints, 0) > 4) and (np.size(prevPoints, 0) == np.size(prevPoints, 0)):
+            H, inliesrs = cv2.estimateAffinePartial2D(prevPoints, currPoints, cv2.RANSAC)
+
+            # Handle downscale
+            if self.downscale > 1.0:
+                H[0, 2] *= self.downscale
+                H[1, 2] *= self.downscale
+        else:
+            print('Warning: not enough matching points')
+
+        # Store to next iteration
+        self.prevFrame = frame.copy()
+        self.prevKeyPoints = copy.copy(keypoints)
+        self.prevDescriptors = copy.copy(descriptors)
+
+        return H
+
+    def applySparseOptFlow(self, raw_frame, detections=None):
+
+        t0 = time.time()
+
+        # Initialize
+        height, width, _ = raw_frame.shape
+        frame = cv2.cvtColor(raw_frame, cv2.COLOR_BGR2GRAY)
+        H = np.eye(2, 3)
+
+        # Downscale image
+        if self.downscale > 1.0:
+            # frame = cv2.GaussianBlur(frame, (3, 3), 1.5)
+            frame = cv2.resize(frame, (width // self.downscale, height // self.downscale))
+
+        # find the keypoints
+        keypoints = cv2.goodFeaturesToTrack(frame, mask=None, **self.feature_params)
+
+        # Handle first frame
+        if not self.initializedFirstFrame:
+            # Initialize data
+            self.prevFrame = frame.copy()
+            self.prevKeyPoints = copy.copy(keypoints)
+
+            # Initialization done
+            self.initializedFirstFrame = True
+
+            return H
+
+        # find correspondences
+        matchedKeypoints, status, err = cv2.calcOpticalFlowPyrLK(self.prevFrame, frame, self.prevKeyPoints, None)
+
+        # leave good correspondences only
+        prevPoints = []
+        currPoints = []
+
+        for i in range(len(status)):
+            if status[i]:
+                prevPoints.append(self.prevKeyPoints[i])
+                currPoints.append(matchedKeypoints[i])
+
+        prevPoints = np.array(prevPoints)
+        currPoints = np.array(currPoints)
+
+        # Find rigid matrix
+        if (np.size(prevPoints, 0) > 4) and (np.size(prevPoints, 0) == np.size(prevPoints, 0)):
+            H, inliesrs = cv2.estimateAffinePartial2D(prevPoints, currPoints, cv2.RANSAC)
+
+            # Handle downscale
+            if self.downscale > 1.0:
+                H[0, 2] *= self.downscale
+                H[1, 2] *= self.downscale
+        else:
+            print('Warning: not enough matching points')
+
+        # Store to next iteration
+        self.prevFrame = frame.copy()
+        self.prevKeyPoints = copy.copy(keypoints)
+
+        t1 = time.time()
+
+        # gmc_line = str(1000 * (t1 - t0)) + "\t" + str(H[0, 0]) + "\t" + str(H[0, 1]) + "\t" + str(
+        #     H[0, 2]) + "\t" + str(H[1, 0]) + "\t" + str(H[1, 1]) + "\t" + str(H[1, 2]) + "\n"
+        # self.gmc_file.write(gmc_line)
+
+        return H
+
+    def applyFile(self, raw_frame, detections=None):
+        line = self.gmcFile.readline()
+        tokens = line.split("\t")
+        H = np.eye(2, 3, dtype=np.float_)
+        H[0, 0] = float(tokens[1])
+        H[0, 1] = float(tokens[2])
+        H[0, 2] = float(tokens[3])
+        H[1, 0] = float(tokens[4])
+        H[1, 1] = float(tokens[5])
+        H[1, 2] = float(tokens[6])
+
+        return H
+
+    def applyCMC(self, frame):
+        # Convert frame to grayscale
+        curr_gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
+
+        # Handle first frame
+        if not self.initializedFirstFrame:
+            # Initialization
+            self.initializedFirstFrame = True
+            self.prev_gray = np.copy(curr_gray)
+            return np.eye(2, 3, dtype=np.float32)  # Return identity matrix for the first frame
+
+        # Detect feature points in previous frame
+        prev_pts = cv2.goodFeaturesToTrack(self.prev_gray, maxCorners=200, qualityLevel=0.01, minDistance=30,
+                                           blockSize=3)
+        # Calculate optical flow (i.e. track feature points)
+        curr_pts, status, err = cv2.calcOpticalFlowPyrLK(self.prev_gray, curr_gray, prev_pts, None)
+
+        if curr_pts is None:
+            return np.eye(2, 3)  # Return identity matrix if no good points are found
+
+        # Sanity check
+        assert prev_pts.shape == curr_pts.shape
+        # Filter only valid points
+        idx = np.where(status == 1)[0]
+        prev_pts = prev_pts[idx]
+        curr_pts = curr_pts[idx]
+        # Find transformation matrix
+        # m, inliers = cv2.estimateAffinePartial2D(prev_pts, curr_pts)
+        m, inliers = cv2.estimateAffine2D(prev_pts, curr_pts)
+        # Update the previous frame and points
+        self.prev_gray = np.copy(curr_gray)
+
+        # Determine camera movement
+        translation_magnitude = np.sqrt(m[0, 2] ** 2 + m[1, 2] ** 2)
+        scaling_factor = np.linalg.det(m[:, :2])
+
+        # # Check if camera has moved based on thresholds
+        # if translation_magnitude < 1.0 and abs(scaling_factor - 1) < 0.1:
+        #     # print("No significant camera movement")
+        #     return np.eye(2, 3)
+
+        return m if m is not None else np.eye(2, 3)  # If estimation fails, return identity matrix
diff --git a/trackers/bytetrack/kalman_filter.py b/trackers/bytetrack/kalman_filter.py
new file mode 100644
index 0000000000000000000000000000000000000000..9909be26b561ab9d8705de484176b5bc56b3b23f
--- /dev/null
+++ b/trackers/bytetrack/kalman_filter.py
@@ -0,0 +1,270 @@
+# vim: expandtab:ts=4:sw=4
+import numpy as np
+import scipy.linalg
+
+
+"""
+Table for the 0.95 quantile of the chi-square distribution with N degrees of
+freedom (contains values for N=1, ..., 9). Taken from MATLAB/Octave's chi2inv
+function and used as Mahalanobis gating threshold.
+"""
+chi2inv95 = {
+    1: 3.8415,
+    2: 5.9915,
+    3: 7.8147,
+    4: 9.4877,
+    5: 11.070,
+    6: 12.592,
+    7: 14.067,
+    8: 15.507,
+    9: 16.919}
+
+
+class KalmanFilter(object):
+    """
+    A simple Kalman filter for tracking bounding boxes in image space.
+
+    The 8-dimensional state space
+
+        x, y, a, h, vx, vy, va, vh
+
+    contains the bounding box center position (x, y), aspect ratio a, height h,
+    and their respective velocities.
+
+    Object motion follows a constant velocity model. The bounding box location
+    (x, y, a, h) is taken as direct observation of the state space (linear
+    observation model).
+
+    """
+
+    def __init__(self):
+        ndim, dt = 4, 1.
+
+        # Create Kalman filter model matrices.
+        self._motion_mat = np.eye(2 * ndim, 2 * ndim)
+        for i in range(ndim):
+            self._motion_mat[i, ndim + i] = dt
+        self._update_mat = np.eye(ndim, 2 * ndim)
+
+        # Motion and observation uncertainty are chosen relative to the current
+        # state estimate. These weights control the amount of uncertainty in
+        # the model. This is a bit hacky.
+        self._std_weight_position = 1. / 20
+        self._std_weight_velocity = 1. / 160
+
+    def initiate(self, measurement):
+        """Create track from unassociated measurement.
+
+        Parameters
+        ----------
+        measurement : ndarray
+            Bounding box coordinates (x, y, a, h) with center position (x, y),
+            aspect ratio a, and height h.
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector (8 dimensional) and covariance matrix (8x8
+            dimensional) of the new track. Unobserved velocities are initialized
+            to 0 mean.
+
+        """
+        mean_pos = measurement
+        mean_vel = np.zeros_like(mean_pos)
+        mean = np.r_[mean_pos, mean_vel]
+
+        std = [
+            2 * self._std_weight_position * measurement[3],
+            2 * self._std_weight_position * measurement[3],
+            1e-2,
+            2 * self._std_weight_position * measurement[3],
+            10 * self._std_weight_velocity * measurement[3],
+            10 * self._std_weight_velocity * measurement[3],
+            1e-5,
+            10 * self._std_weight_velocity * measurement[3]]
+        covariance = np.diag(np.square(std))
+        return mean, covariance
+
+    def predict(self, mean, covariance):
+        """Run Kalman filter prediction step.
+
+        Parameters
+        ----------
+        mean : ndarray
+            The 8 dimensional mean vector of the object state at the previous
+            time step.
+        covariance : ndarray
+            The 8x8 dimensional covariance matrix of the object state at the
+            previous time step.
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector and covariance matrix of the predicted
+            state. Unobserved velocities are initialized to 0 mean.
+
+        """
+        std_pos = [
+            self._std_weight_position * mean[3],
+            self._std_weight_position * mean[3],
+            1e-2,
+            self._std_weight_position * mean[3]]
+        std_vel = [
+            self._std_weight_velocity * mean[3],
+            self._std_weight_velocity * mean[3],
+            1e-5,
+            self._std_weight_velocity * mean[3]]
+        motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))
+
+        #mean = np.dot(self._motion_mat, mean)
+        mean = np.dot(mean, self._motion_mat.T)
+        covariance = np.linalg.multi_dot((
+            self._motion_mat, covariance, self._motion_mat.T)) + motion_cov
+
+        return mean, covariance
+
+    def project(self, mean, covariance):
+        """Project state distribution to measurement space.
+
+        Parameters
+        ----------
+        mean : ndarray
+            The state's mean vector (8 dimensional array).
+        covariance : ndarray
+            The state's covariance matrix (8x8 dimensional).
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the projected mean and covariance matrix of the given state
+            estimate.
+
+        """
+        std = [
+            self._std_weight_position * mean[3],
+            self._std_weight_position * mean[3],
+            1e-1,
+            self._std_weight_position * mean[3]]
+        innovation_cov = np.diag(np.square(std))
+
+        mean = np.dot(self._update_mat, mean)
+        covariance = np.linalg.multi_dot((
+            self._update_mat, covariance, self._update_mat.T))
+        return mean, covariance + innovation_cov
+
+    def multi_predict(self, mean, covariance):
+        """Run Kalman filter prediction step (Vectorized version).
+        Parameters
+        ----------
+        mean : ndarray
+            The Nx8 dimensional mean matrix of the object states at the previous
+            time step.
+        covariance : ndarray
+            The Nx8x8 dimensional covariance matrics of the object states at the
+            previous time step.
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector and covariance matrix of the predicted
+            state. Unobserved velocities are initialized to 0 mean.
+        """
+        std_pos = [
+            self._std_weight_position * mean[:, 3],
+            self._std_weight_position * mean[:, 3],
+            1e-2 * np.ones_like(mean[:, 3]),
+            self._std_weight_position * mean[:, 3]]
+        std_vel = [
+            self._std_weight_velocity * mean[:, 3],
+            self._std_weight_velocity * mean[:, 3],
+            1e-5 * np.ones_like(mean[:, 3]),
+            self._std_weight_velocity * mean[:, 3]]
+        sqr = np.square(np.r_[std_pos, std_vel]).T
+
+        motion_cov = []
+        for i in range(len(mean)):
+            motion_cov.append(np.diag(sqr[i]))
+        motion_cov = np.asarray(motion_cov)
+
+        mean = np.dot(mean, self._motion_mat.T)
+        left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
+        covariance = np.dot(left, self._motion_mat.T) + motion_cov
+
+        return mean, covariance
+
+    def update(self, mean, covariance, measurement):
+        """Run Kalman filter correction step.
+
+        Parameters
+        ----------
+        mean : ndarray
+            The predicted state's mean vector (8 dimensional).
+        covariance : ndarray
+            The state's covariance matrix (8x8 dimensional).
+        measurement : ndarray
+            The 4 dimensional measurement vector (x, y, a, h), where (x, y)
+            is the center position, a the aspect ratio, and h the height of the
+            bounding box.
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the measurement-corrected state distribution.
+
+        """
+        projected_mean, projected_cov = self.project(mean, covariance)
+
+        chol_factor, lower = scipy.linalg.cho_factor(
+            projected_cov, lower=True, check_finite=False)
+        kalman_gain = scipy.linalg.cho_solve(
+            (chol_factor, lower), np.dot(covariance, self._update_mat.T).T,
+            check_finite=False).T
+        innovation = measurement - projected_mean
+
+        new_mean = mean + np.dot(innovation, kalman_gain.T)
+        new_covariance = covariance - np.linalg.multi_dot((
+            kalman_gain, projected_cov, kalman_gain.T))
+        return new_mean, new_covariance
+
+    def gating_distance(self, mean, covariance, measurements,
+                        only_position=False, metric='maha'):
+        """Compute gating distance between state distribution and measurements.
+        A suitable distance threshold can be obtained from `chi2inv95`. If
+        `only_position` is False, the chi-square distribution has 4 degrees of
+        freedom, otherwise 2.
+        Parameters
+        ----------
+        mean : ndarray
+            Mean vector over the state distribution (8 dimensional).
+        covariance : ndarray
+            Covariance of the state distribution (8x8 dimensional).
+        measurements : ndarray
+            An Nx4 dimensional matrix of N measurements, each in
+            format (x, y, a, h) where (x, y) is the bounding box center
+            position, a the aspect ratio, and h the height.
+        only_position : Optional[bool]
+            If True, distance computation is done with respect to the bounding
+            box center position only.
+        Returns
+        -------
+        ndarray
+            Returns an array of length N, where the i-th element contains the
+            squared Mahalanobis distance between (mean, covariance) and
+            `measurements[i]`.
+        """
+        mean, covariance = self.project(mean, covariance)
+        if only_position:
+            mean, covariance = mean[:2], covariance[:2, :2]
+            measurements = measurements[:, :2]
+
+        d = measurements - mean
+        if metric == 'gaussian':
+            return np.sum(d * d, axis=1)
+        elif metric == 'maha':
+            cholesky_factor = np.linalg.cholesky(covariance)
+            z = scipy.linalg.solve_triangular(
+                cholesky_factor, d.T, lower=True, check_finite=False,
+                overwrite_b=True)
+            squared_maha = np.sum(z * z, axis=0)
+            return squared_maha
+        else:
+            raise ValueError('invalid distance metric')
\ No newline at end of file
diff --git a/trackers/bytetrack/matching.py b/trackers/bytetrack/matching.py
new file mode 100644
index 0000000000000000000000000000000000000000..06cca8528d701226d007e66f5aff38de0ae3de0e
--- /dev/null
+++ b/trackers/bytetrack/matching.py
@@ -0,0 +1,219 @@
+import numpy as np
+import scipy
+import lap
+from scipy.spatial.distance import cdist
+
+from cython_bbox import bbox_overlaps as bbox_ious
+from . import kalman_filter
+
+
+def merge_matches(m1, m2, shape):
+    O,P,Q = shape
+    m1 = np.asarray(m1)
+    m2 = np.asarray(m2)
+
+    M1 = scipy.sparse.coo_matrix((np.ones(len(m1)), (m1[:, 0], m1[:, 1])), shape=(O, P))
+    M2 = scipy.sparse.coo_matrix((np.ones(len(m2)), (m2[:, 0], m2[:, 1])), shape=(P, Q))
+
+    mask = M1*M2
+    match = mask.nonzero()
+    match = list(zip(match[0], match[1]))
+    unmatched_O = tuple(set(range(O)) - set([i for i, j in match]))
+    unmatched_Q = tuple(set(range(Q)) - set([j for i, j in match]))
+
+    return match, unmatched_O, unmatched_Q
+
+
+def _indices_to_matches(cost_matrix, indices, thresh):
+    matched_cost = cost_matrix[tuple(zip(*indices))]
+    matched_mask = (matched_cost <= thresh)
+
+    matches = indices[matched_mask]
+    unmatched_a = tuple(set(range(cost_matrix.shape[0])) - set(matches[:, 0]))
+    unmatched_b = tuple(set(range(cost_matrix.shape[1])) - set(matches[:, 1]))
+
+    return matches, unmatched_a, unmatched_b
+
+
+def linear_assignment(cost_matrix, thresh):
+    if cost_matrix.size == 0:
+        return np.empty((0, 2), dtype=int), tuple(range(cost_matrix.shape[0])), tuple(range(cost_matrix.shape[1]))
+    matches, unmatched_a, unmatched_b = [], [], []
+    cost, x, y = lap.lapjv(cost_matrix, extend_cost=True, cost_limit=thresh)
+    for ix, mx in enumerate(x):
+        if mx >= 0:
+            matches.append([ix, mx])
+    unmatched_a = np.where(x < 0)[0]
+    unmatched_b = np.where(y < 0)[0]
+    matches = np.asarray(matches)
+    return matches, unmatched_a, unmatched_b
+
+
+def ious(atlbrs, btlbrs):
+    """
+    Compute cost based on IoU
+    :type atlbrs: list[tlbr] | np.ndarray
+    :type atlbrs: list[tlbr] | np.ndarray
+
+    :rtype ious np.ndarray
+    """
+    ious = np.zeros((len(atlbrs), len(btlbrs)), dtype=float)
+    if ious.size == 0:
+        return ious
+
+    ious = bbox_ious(
+        np.ascontiguousarray(atlbrs, dtype=float),
+        np.ascontiguousarray(btlbrs, dtype=float)
+    )
+
+    return ious
+
+
+def giou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    if min(len(bboxes1), len(bboxes2)) == 0:
+        return np.zeros((len(bboxes1), len(bboxes2)), dtype=float)
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    union = ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)
+    iou = wh / union
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+    wc = xxc2 - xxc1
+    hc = yyc2 - yyc1
+    assert((wc > 0).all() and (hc > 0).all())
+    area_enclose = wc * hc
+    giou = iou - (area_enclose - union) / area_enclose
+    giou = (giou + 1.)/2.0 # resize from (-1,1) to (0,1)
+    return giou
+
+
+def iou_distance(atracks, btracks, giou=False):
+    """
+    Compute cost based on IoU
+    :type atracks: list[STrack]
+    :type btracks: list[STrack]
+
+    :rtype cost_matrix np.ndarray
+    """
+
+    if (len(atracks)>0 and isinstance(atracks[0], np.ndarray)) or (len(btracks) > 0 and isinstance(btracks[0], np.ndarray)):
+        atlbrs = atracks
+        btlbrs = btracks
+    else:
+        atlbrs = [track.tlbr for track in atracks]
+        btlbrs = [track.tlbr for track in btracks]
+    _ious = ious(atlbrs, btlbrs)
+    if giou:
+        _ious = giou_batch(atlbrs, btlbrs)
+    cost_matrix = 1 - _ious
+
+    return cost_matrix
+
+def v_iou_distance(atracks, btracks):
+    """
+    Compute cost based on IoU
+    :type atracks: list[STrack]
+    :type btracks: list[STrack]
+
+    :rtype cost_matrix np.ndarray
+    """
+
+    if (len(atracks)>0 and isinstance(atracks[0], np.ndarray)) or (len(btracks) > 0 and isinstance(btracks[0], np.ndarray)):
+        atlbrs = atracks
+        btlbrs = btracks
+    else:
+        atlbrs = [track.tlwh_to_tlbr(track.pred_bbox) for track in atracks]
+        btlbrs = [track.tlwh_to_tlbr(track.pred_bbox) for track in btracks]
+    _ious = ious(atlbrs, btlbrs)
+    cost_matrix = 1 - _ious
+
+    return cost_matrix
+
+def embedding_distance(tracks, detections, metric='cosine'):
+    """
+    :param tracks: list[STrack]
+    :param detections: list[BaseTrack]
+    :param metric:
+    :return: cost_matrix np.ndarray
+    """
+
+    cost_matrix = np.zeros((len(tracks), len(detections)), dtype=float)
+    if cost_matrix.size == 0:
+        return cost_matrix
+    det_features = np.asarray([track.curr_feat for track in detections], dtype=float)
+    #for i, track in enumerate(tracks):
+        #cost_matrix[i, :] = np.maximum(0.0, cdist(track.smooth_feat.reshape(1,-1), det_features, metric))
+    track_features = np.asarray([track.smooth_feat for track in tracks], dtype=float)
+    cost_matrix = np.maximum(0.0, cdist(track_features, det_features, metric))  # Nomalized features
+    return cost_matrix
+
+
+def gate_cost_matrix(kf, cost_matrix, tracks, detections, only_position=False):
+    if cost_matrix.size == 0:
+        return cost_matrix
+    gating_dim = 2 if only_position else 4
+    gating_threshold = kalman_filter.chi2inv95[gating_dim]
+    measurements = np.asarray([det.to_xyah() for det in detections])
+    for row, track in enumerate(tracks):
+        gating_distance = kf.gating_distance(
+            track.mean, track.covariance, measurements, only_position)
+        cost_matrix[row, gating_distance > gating_threshold] = np.inf
+    return cost_matrix
+
+
+def fuse_motion(kf, cost_matrix, tracks, detections, only_position=False, lambda_=0.98):
+    if cost_matrix.size == 0:
+        return cost_matrix
+    gating_dim = 2 if only_position else 4
+    gating_threshold = kalman_filter.chi2inv95[gating_dim]
+    measurements = np.asarray([det.to_xyah() for det in detections])
+    for row, track in enumerate(tracks):
+        gating_distance = kf.gating_distance(
+            track.mean, track.covariance, measurements, only_position, metric='maha')
+        cost_matrix[row, gating_distance > gating_threshold] = np.inf
+        cost_matrix[row] = lambda_ * cost_matrix[row] + (1 - lambda_) * gating_distance
+    return cost_matrix
+
+
+def fuse_iou(cost_matrix, tracks, detections):
+    if cost_matrix.size == 0:
+        return cost_matrix
+    reid_sim = 1 - cost_matrix
+    iou_dist = iou_distance(tracks, detections)
+    iou_sim = 1 - iou_dist
+    fuse_sim = reid_sim * (1 + iou_sim) / 2
+    det_scores = np.array([det.score for det in detections])
+    det_scores = np.expand_dims(det_scores, axis=0).repeat(cost_matrix.shape[0], axis=0)
+    #fuse_sim = fuse_sim * (1 + det_scores) / 2
+    fuse_cost = 1 - fuse_sim
+    return fuse_cost
+
+
+def fuse_score(cost_matrix, detections):
+    if cost_matrix.size == 0:
+        return cost_matrix
+    iou_sim = 1 - cost_matrix
+    det_scores = np.array([det.score for det in detections])
+    det_scores = np.expand_dims(det_scores, axis=0).repeat(cost_matrix.shape[0], axis=0)
+    fuse_sim = iou_sim * det_scores
+    fuse_cost = 1 - fuse_sim
+    return fuse_cost
\ No newline at end of file
diff --git a/trackers/deepsort/deepsort.py b/trackers/deepsort/deepsort.py
new file mode 100644
index 0000000000000000000000000000000000000000..1a87db67a16d0ae4343e2f63801111aa36a88cdb
--- /dev/null
+++ b/trackers/deepsort/deepsort.py
@@ -0,0 +1,287 @@
+import numpy as np
+import cv2
+import os
+
+from . import kalman_filter, linear_assignment, iou_matching
+from .detection import Detection
+from .track import Track
+
+
+def _cosine_distance(a, b, data_is_normalized=False):
+    if not data_is_normalized:
+        a = np.asarray(a) / np.linalg.norm(a, axis=1, keepdims=True)
+        b = np.asarray(b) / np.linalg.norm(b, axis=1, keepdims=True)
+    return 1.0 - np.dot(a, b.T)
+
+
+def _nn_cosine_distance(x, y):
+    distances = _cosine_distance(x, y)
+    return distances.min(axis=0)
+
+
+class Tracker:
+    def __init__(self, metric, max_iou_distance=0.7, max_age=70, n_init=3):
+        self.metric = metric
+        self.max_iou_distance = max_iou_distance
+        self.max_age = max_age
+        self.n_init = n_init
+
+        self.kf = kalman_filter.KalmanFilter()
+        self.tracks = []
+        self._next_id = 1
+
+    def predict(self):
+        """Propagate track state distributions one time step forward.
+        This function should be called once every time step, before `update`.
+        """
+        for track in self.tracks:
+            track.predict(self.kf)
+
+    def increment_ages(self):
+        for track in self.tracks:
+            track.increment_age()
+            track.mark_missed()
+
+    def update(self, detections, classes):
+        """Perform measurement update and track management.
+        Parameters
+        ----------
+        detections : List[deep_sort.detection.Detection]
+            A list of detections at the current time step.
+        """
+        # Run matching cascade.
+        matches, unmatched_tracks, unmatched_detections = self._match(detections)
+
+        # Update track set.
+        for track_idx, detection_idx in matches:
+            self.tracks[track_idx].update(self.kf, detections[detection_idx])
+        for track_idx in unmatched_tracks:
+            self.tracks[track_idx].mark_missed()
+        for detection_idx in unmatched_detections:
+            self._initiate_track(detections[detection_idx], classes[detection_idx].item())
+        self.tracks = [t for t in self.tracks if not t.is_deleted()]
+
+        # Update distance metric.
+        active_targets = [t.track_id for t in self.tracks if t.is_confirmed()]
+        features, targets = [], []
+        for track in self.tracks:
+            if not track.is_confirmed():
+                continue
+            features += track.features
+            targets += [track.track_id for _ in track.features]
+            track.features = []
+        self.metric.partial_fit(np.asarray(features), np.asarray(targets), active_targets)
+
+    def _match(self, detections):
+        def gated_metric(tracks, dets, track_indices, detection_indices):
+            features = np.array([dets[i].feature for i in detection_indices])
+            targets = np.array([tracks[i].track_id for i in track_indices])
+            cost_matrix = self.metric.distance(features, targets)
+            cost_matrix = linear_assignment.gate_cost_matrix(
+                self.kf, cost_matrix, tracks, dets, track_indices, detection_indices
+            )
+
+            return cost_matrix
+
+        # Split track set into confirmed and unconfirmed tracks.
+        confirmed_tracks = [i for i, t in enumerate(self.tracks) if t.is_confirmed()]
+        unconfirmed_tracks = [i for i, t in enumerate(self.tracks) if not t.is_confirmed()]
+
+        # Associate confirmed tracks using appearance features.
+        (matches_a, unmatched_tracks_a, unmatched_detections,) = linear_assignment.matching_cascade(
+            gated_metric,
+            self.metric.matching_threshold,
+            self.max_age,
+            self.tracks,
+            detections,
+            confirmed_tracks,
+        )
+
+        # Associate remaining tracks together with unconfirmed tracks using IOU.
+        iou_track_candidates = unconfirmed_tracks + [
+            k for k in unmatched_tracks_a if self.tracks[k].time_since_update == 1
+        ]
+        unmatched_tracks_a = [k for k in unmatched_tracks_a if self.tracks[k].time_since_update != 1]
+        (matches_b, unmatched_tracks_b, unmatched_detections,) = linear_assignment.min_cost_matching(
+            iou_matching.iou_cost,
+            self.max_iou_distance,
+            self.tracks,
+            detections,
+            iou_track_candidates,
+            unmatched_detections,
+        )
+
+        matches = matches_a + matches_b
+        unmatched_tracks = list(set(unmatched_tracks_a + unmatched_tracks_b))
+        return matches, unmatched_tracks, unmatched_detections
+
+    def _initiate_track(self, detection, class_id):
+        mean, covariance = self.kf.initiate(detection.to_xyah())
+        self.tracks.append(
+            Track(
+                mean,
+                covariance,
+                self._next_id,
+                class_id,
+                self.n_init,
+                self.max_age,
+                detection.feature,
+            )
+        )
+        self._next_id += 1
+
+
+class NearestNeighborDistanceMetric(object):
+    def __init__(self, metric, matching_threshold, budget=None):
+
+        if metric == "cosine":
+            self._metric = _nn_cosine_distance
+        else:
+            raise ValueError("Invalid metric; must be either 'euclidean' or 'cosine'")
+        self.matching_threshold = matching_threshold
+        self.budget = budget
+        self.samples = {}
+
+    def partial_fit(self, features, targets, active_targets):
+        for feature, target in zip(features, targets):
+            self.samples.setdefault(target, []).append(feature)
+            if self.budget is not None:
+                self.samples[target] = self.samples[target][-self.budget :]
+        self.samples = {k: self.samples[k] for k in active_targets}
+
+    def distance(self, features, targets):
+        cost_matrix = np.zeros((len(targets), len(features)))
+        for i, target in enumerate(targets):
+            cost_matrix[i, :] = self._metric(self.samples[target], features)
+        return cost_matrix
+
+
+class DeepSort(object):
+    def __init__(
+        self,
+        max_dist=0.1,
+        min_confidence=0.3,
+        nms_max_overlap=1.0,
+        max_iou_distance=0.7,
+        max_age=30,
+        n_init=3,
+        nn_budget=100,
+        use_cuda=True,
+    ):
+        self.min_confidence = min_confidence
+        self.nms_max_overlap = nms_max_overlap
+
+        # self.extractor = Extractor(model_path, use_cuda=use_cuda)
+
+        max_cosine_distance = max_dist
+        metric = NearestNeighborDistanceMetric("cosine", max_cosine_distance, nn_budget)
+        self.tracker = Tracker(metric, max_iou_distance=max_iou_distance, max_age=max_age, n_init=n_init)
+
+    def update(self, fdets, img):
+        #####
+        remain_inds = fdets[:, 4] > self.min_confidence
+        dets, id_feature = fdets[remain_inds, 0:5], fdets[remain_inds, 5:]
+        dets[:, 2:4] = dets[:, 2:4] - dets[:, 0:2]
+        #####
+        detections = [
+            Detection(dets[i, 0:4], conf, id_feature[i])
+            for i, conf in enumerate(dets[:, 4])
+        ]
+        classes = np.zeros((len(detections),))
+
+        # update tracker
+        self.tracker.predict()
+        self.tracker.update(detections, classes)
+
+        # output bbox identities
+        outputs = []
+        for track in self.tracker.tracks:
+            if not track.is_confirmed() or track.time_since_update > 1:
+                continue
+            track.tlwh = track.to_tlwh()
+            outputs.append(track)
+        return outputs
+
+    """
+    TODO:
+        Convert bbox from xc_yc_w_h to xtl_ytl_w_h
+    Thanks JieChen91@github.com for reporting this bug!
+    """
+
+    @staticmethod
+    def _xywh_to_tlwh(bbox_xywh):
+        if isinstance(bbox_xywh, np.ndarray):
+            bbox_tlwh = bbox_xywh.copy()
+        elif isinstance(bbox_xywh, torch.Tensor):
+            bbox_tlwh = bbox_xywh.clone()
+        bbox_tlwh[:, 0] = bbox_xywh[:, 0] - bbox_xywh[:, 2] / 2.0
+        bbox_tlwh[:, 1] = bbox_xywh[:, 1] - bbox_xywh[:, 3] / 2.0
+        return bbox_tlwh
+
+    @staticmethod
+    def _xyxy_to_tlwh_array(bbox_xyxy):
+        if isinstance(bbox_xyxy, np.ndarray):
+            bbox_tlwh = bbox_xyxy.copy()
+        elif isinstance(bbox_xyxy, torch.Tensor):
+            bbox_tlwh = bbox_xyxy.clone()
+        bbox_tlwh[:, 2] = bbox_xyxy[:, 2] - bbox_xyxy[:, 0]
+        bbox_tlwh[:, 3] = bbox_xyxy[:, 3] - bbox_xyxy[:, 1]
+        return bbox_tlwh
+
+    def _xywh_to_xyxy(self, bbox_xywh):
+        x, y, w, h = bbox_xywh
+        x1 = max(int(x - w / 2), 0)
+        x2 = min(int(x + w / 2), self.width - 1)
+        y1 = max(int(y - h / 2), 0)
+        y2 = min(int(y + h / 2), self.height - 1)
+        return x1, y1, x2, y2
+
+    def _tlwh_to_xyxy(self, bbox_tlwh):
+        """
+        TODO:
+            Convert bbox from xtl_ytl_w_h to xc_yc_w_h
+        Thanks JieChen91@github.com for reporting this bug!
+        """
+        x, y, w, h = bbox_tlwh
+        x1 = max(int(x), 0)
+        x2 = min(int(x + w), self.width - 1)
+        y1 = max(int(y), 0)
+        y2 = min(int(y + h), self.height - 1)
+        return x1, y1, x2, y2
+
+    def _tlwh_to_xyxy_noclip(self, bbox_tlwh):
+        """
+        TODO:
+            Convert bbox from xtl_ytl_w_h to xc_yc_w_h
+        Thanks JieChen91@github.com for reporting this bug!
+        """
+        x, y, w, h = bbox_tlwh
+        x1 = x
+        x2 = x + w
+        y1 = y
+        y2 = y + h
+        return x1, y1, x2, y2
+
+    def increment_ages(self):
+        self.tracker.increment_ages()
+
+    def _xyxy_to_tlwh(self, bbox_xyxy):
+        x1, y1, x2, y2 = bbox_xyxy
+
+        t = x1
+        l = y1
+        w = int(x2 - x1)
+        h = int(y2 - y1)
+        return t, l, w, h
+
+    def _get_features(self, bbox_xywh, ori_img):
+        im_crops = []
+        for box in bbox_xywh:
+            x1, y1, x2, y2 = self._tlwh_to_xyxy(box)
+            im = ori_img[y1:y2, x1:x2]
+            im_crops.append(im)
+        if im_crops:
+            features = self.extractor(im_crops)
+        else:
+            features = np.array([])
+        return features
diff --git a/trackers/deepsort/detection.py b/trackers/deepsort/detection.py
new file mode 100644
index 0000000000000000000000000000000000000000..2101049adb344ab834bc9b8d32d0c41847cc6d35
--- /dev/null
+++ b/trackers/deepsort/detection.py
@@ -0,0 +1,46 @@
+# vim: expandtab:ts=4:sw=4
+import numpy as np
+
+
+class Detection(object):
+    """
+    This class represents a bounding box detection in a single image.
+    Parameters
+    ----------
+    tlwh : array_like
+        Bounding box in format `(x, y, w, h)`.
+    confidence : float
+        Detector confidence score.
+    feature : array_like
+        A feature vector that describes the object contained in this image.
+    Attributes
+    ----------
+    tlwh : ndarray
+        Bounding box in format `(top left x, top left y, width, height)`.
+    confidence : ndarray
+        Detector confidence score.
+    feature : ndarray | NoneType
+        A feature vector that describes the object contained in this image.
+    """
+
+    def __init__(self, tlwh, confidence, feature):
+        self.tlwh = np.asarray(tlwh, dtype=np.float)
+        self.confidence = float(confidence)
+        self.feature = np.asarray(feature, dtype=np.float32)
+
+    def to_tlbr(self):
+        """Convert bounding box to format `(min x, min y, max x, max y)`, i.e.,
+        `(top left, bottom right)`.
+        """
+        ret = self.tlwh.copy()
+        ret[2:] += ret[:2]
+        return ret
+
+    def to_xyah(self):
+        """Convert bounding box to format `(center x, center y, aspect ratio,
+        height)`, where the aspect ratio is `width / height`.
+        """
+        ret = self.tlwh.copy()
+        ret[:2] += ret[2:] / 2
+        ret[2] /= ret[3]
+        return ret
diff --git a/trackers/deepsort/iou_matching.py b/trackers/deepsort/iou_matching.py
new file mode 100644
index 0000000000000000000000000000000000000000..4d488e26c57acd492985c7f04045f2a3dc90700d
--- /dev/null
+++ b/trackers/deepsort/iou_matching.py
@@ -0,0 +1,78 @@
+# vim: expandtab:ts=4:sw=4
+from __future__ import absolute_import
+import numpy as np
+from . import linear_assignment
+
+
+def iou(bbox, candidates):
+    """Computer intersection over union.
+    Parameters
+    ----------
+    bbox : ndarray
+        A bounding box in format `(top left x, top left y, width, height)`.
+    candidates : ndarray
+        A matrix of candidate bounding boxes (one per row) in the same format
+        as `bbox`.
+    Returns
+    -------
+    ndarray
+        The intersection over union in [0, 1] between the `bbox` and each
+        candidate. A higher score means a larger fraction of the `bbox` is
+        occluded by the candidate.
+    """
+    bbox_tl, bbox_br = bbox[:2], bbox[:2] + bbox[2:]
+    candidates_tl = candidates[:, :2]
+    candidates_br = candidates[:, :2] + candidates[:, 2:]
+
+    tl = np.c_[
+        np.maximum(bbox_tl[0], candidates_tl[:, 0])[:, np.newaxis],
+        np.maximum(bbox_tl[1], candidates_tl[:, 1])[:, np.newaxis],
+    ]
+    br = np.c_[
+        np.minimum(bbox_br[0], candidates_br[:, 0])[:, np.newaxis],
+        np.minimum(bbox_br[1], candidates_br[:, 1])[:, np.newaxis],
+    ]
+    wh = np.maximum(0.0, br - tl)
+
+    area_intersection = wh.prod(axis=1)
+    area_bbox = bbox[2:].prod()
+    area_candidates = candidates[:, 2:].prod(axis=1)
+    return area_intersection / (area_bbox + area_candidates - area_intersection)
+
+
+def iou_cost(tracks, detections, track_indices=None, detection_indices=None):
+    """An intersection over union distance metric.
+    Parameters
+    ----------
+    tracks : List[deep_sort.track.Track]
+        A list of tracks.
+    detections : List[deep_sort.detection.Detection]
+        A list of detections.
+    track_indices : Optional[List[int]]
+        A list of indices to tracks that should be matched. Defaults to
+        all `tracks`.
+    detection_indices : Optional[List[int]]
+        A list of indices to detections that should be matched. Defaults
+        to all `detections`.
+    Returns
+    -------
+    ndarray
+        Returns a cost matrix of shape
+        len(track_indices), len(detection_indices) where entry (i, j) is
+        `1 - iou(tracks[track_indices[i]], detections[detection_indices[j]])`.
+    """
+    if track_indices is None:
+        track_indices = np.arange(len(tracks))
+    if detection_indices is None:
+        detection_indices = np.arange(len(detections))
+
+    cost_matrix = np.zeros((len(track_indices), len(detection_indices)))
+    for row, track_idx in enumerate(track_indices):
+        if tracks[track_idx].time_since_update > 1:
+            cost_matrix[row, :] = linear_assignment.INFTY_COST
+            continue
+
+        bbox = tracks[track_idx].to_tlwh()
+        candidates = np.asarray([detections[i].tlwh for i in detection_indices])
+        cost_matrix[row, :] = 1.0 - iou(bbox, candidates)
+    return cost_matrix
diff --git a/trackers/deepsort/kalman_filter.py b/trackers/deepsort/kalman_filter.py
new file mode 100644
index 0000000000000000000000000000000000000000..d1565edc75c5ea7c0fd893252232c2f4b74887ae
--- /dev/null
+++ b/trackers/deepsort/kalman_filter.py
@@ -0,0 +1,208 @@
+# vim: expandtab:ts=4:sw=4
+import numpy as np
+import scipy.linalg
+
+
+"""
+Table for the 0.95 quantile of the chi-square distribution with N degrees of
+freedom (contains values for N=1, ..., 9). Taken from MATLAB/Octave's chi2inv
+function and used as Mahalanobis gating threshold.
+"""
+chi2inv95 = {
+    1: 3.8415,
+    2: 5.9915,
+    3: 7.8147,
+    4: 9.4877,
+    5: 11.070,
+    6: 12.592,
+    7: 14.067,
+    8: 15.507,
+    9: 16.919,
+}
+
+
+class KalmanFilter(object):
+    """
+    A simple Kalman filter for tracking bounding boxes in image space.
+    The 8-dimensional state space
+        x, y, a, h, vx, vy, va, vh
+    contains the bounding box center position (x, y), aspect ratio a, height h,
+    and their respective velocities.
+    Object motion follows a constant velocity model. The bounding box location
+    (x, y, a, h) is taken as direct observation of the state space (linear
+    observation model).
+    """
+
+    def __init__(self):
+        ndim, dt = 4, 1.0
+
+        # Create Kalman filter model matrices.
+        self._motion_mat = np.eye(2 * ndim, 2 * ndim)
+        for i in range(ndim):
+            self._motion_mat[i, ndim + i] = dt
+        self._update_mat = np.eye(ndim, 2 * ndim)
+
+        # Motion and observation uncertainty are chosen relative to the current
+        # state estimate. These weights control the amount of uncertainty in
+        # the model. This is a bit hacky.
+        self._std_weight_position = 1.0 / 20
+        self._std_weight_velocity = 1.0 / 160
+
+    def initiate(self, measurement):
+        """Create track from unassociated measurement.
+        Parameters
+        ----------
+        measurement : ndarray
+            Bounding box coordinates (x, y, a, h) with center position (x, y),
+            aspect ratio a, and height h.
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector (8 dimensional) and covariance matrix (8x8
+            dimensional) of the new track. Unobserved velocities are initialized
+            to 0 mean.
+        """
+        mean_pos = measurement
+        mean_vel = np.zeros_like(mean_pos)
+        mean = np.r_[mean_pos, mean_vel]
+
+        std = [
+            2 * self._std_weight_position * measurement[3],
+            2 * self._std_weight_position * measurement[3],
+            1e-2,
+            2 * self._std_weight_position * measurement[3],
+            10 * self._std_weight_velocity * measurement[3],
+            10 * self._std_weight_velocity * measurement[3],
+            1e-5,
+            10 * self._std_weight_velocity * measurement[3],
+        ]
+        covariance = np.diag(np.square(std))
+        return mean, covariance
+
+    def predict(self, mean, covariance):
+        """Run Kalman filter prediction step.
+        Parameters
+        ----------
+        mean : ndarray
+            The 8 dimensional mean vector of the object state at the previous
+            time step.
+        covariance : ndarray
+            The 8x8 dimensional covariance matrix of the object state at the
+            previous time step.
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector and covariance matrix of the predicted
+            state. Unobserved velocities are initialized to 0 mean.
+        """
+        std_pos = [
+            self._std_weight_position * mean[3],
+            self._std_weight_position * mean[3],
+            1e-2,
+            self._std_weight_position * mean[3],
+        ]
+        std_vel = [
+            self._std_weight_velocity * mean[3],
+            self._std_weight_velocity * mean[3],
+            1e-5,
+            self._std_weight_velocity * mean[3],
+        ]
+        motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))
+
+        mean = np.dot(self._motion_mat, mean)
+        covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov
+
+        return mean, covariance
+
+    def project(self, mean, covariance):
+        """Project state distribution to measurement space.
+        Parameters
+        ----------
+        mean : ndarray
+            The state's mean vector (8 dimensional array).
+        covariance : ndarray
+            The state's covariance matrix (8x8 dimensional).
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the projected mean and covariance matrix of the given state
+            estimate.
+        """
+        std = [
+            self._std_weight_position * mean[3],
+            self._std_weight_position * mean[3],
+            1e-1,
+            self._std_weight_position * mean[3],
+        ]
+        innovation_cov = np.diag(np.square(std))
+
+        mean = np.dot(self._update_mat, mean)
+        covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
+        return mean, covariance + innovation_cov
+
+    def update(self, mean, covariance, measurement):
+        """Run Kalman filter correction step.
+        Parameters
+        ----------
+        mean : ndarray
+            The predicted state's mean vector (8 dimensional).
+        covariance : ndarray
+            The state's covariance matrix (8x8 dimensional).
+        measurement : ndarray
+            The 4 dimensional measurement vector (x, y, a, h), where (x, y)
+            is the center position, a the aspect ratio, and h the height of the
+            bounding box.
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the measurement-corrected state distribution.
+        """
+        projected_mean, projected_cov = self.project(mean, covariance)
+
+        chol_factor, lower = scipy.linalg.cho_factor(projected_cov, lower=True, check_finite=False)
+        kalman_gain = scipy.linalg.cho_solve(
+            (chol_factor, lower),
+            np.dot(covariance, self._update_mat.T).T,
+            check_finite=False,
+        ).T
+        innovation = measurement - projected_mean
+
+        new_mean = mean + np.dot(innovation, kalman_gain.T)
+        new_covariance = covariance - np.linalg.multi_dot((kalman_gain, projected_cov, kalman_gain.T))
+        return new_mean, new_covariance
+
+    def gating_distance(self, mean, covariance, measurements, only_position=False):
+        """Compute gating distance between state distribution and measurements.
+        A suitable distance threshold can be obtained from `chi2inv95`. If
+        `only_position` is False, the chi-square distribution has 4 degrees of
+        freedom, otherwise 2.
+        Parameters
+        ----------
+        mean : ndarray
+            Mean vector over the state distribution (8 dimensional).
+        covariance : ndarray
+            Covariance of the state distribution (8x8 dimensional).
+        measurements : ndarray
+            An Nx4 dimensional matrix of N measurements, each in
+            format (x, y, a, h) where (x, y) is the bounding box center
+            position, a the aspect ratio, and h the height.
+        only_position : Optional[bool]
+            If True, distance computation is done with respect to the bounding
+            box center position only.
+        Returns
+        -------
+        ndarray
+            Returns an array of length N, where the i-th element contains the
+            squared Mahalanobis distance between (mean, covariance) and
+            `measurements[i]`.
+        """
+        mean, covariance = self.project(mean, covariance)
+        if only_position:
+            mean, covariance = mean[:2], covariance[:2, :2]
+            measurements = measurements[:, :2]
+
+        cholesky_factor = np.linalg.cholesky(covariance)
+        d = measurements - mean
+        z = scipy.linalg.solve_triangular(cholesky_factor, d.T, lower=True, check_finite=False, overwrite_b=True)
+        squared_maha = np.sum(z * z, axis=0)
+        return squared_maha
diff --git a/trackers/deepsort/linear_assignment.py b/trackers/deepsort/linear_assignment.py
new file mode 100644
index 0000000000000000000000000000000000000000..407ba85efbb43ff3f7ba01bc0571812c3ec79e31
--- /dev/null
+++ b/trackers/deepsort/linear_assignment.py
@@ -0,0 +1,199 @@
+from __future__ import absolute_import
+import numpy as np
+
+# from sklearn.utils.linear_assignment_ import linear_assignment
+from scipy.optimize import linear_sum_assignment as linear_assignment
+from . import kalman_filter
+
+
+INFTY_COST = 1e5
+
+
+def min_cost_matching(
+    distance_metric,
+    max_distance,
+    tracks,
+    detections,
+    track_indices=None,
+    detection_indices=None,
+):
+    """Solve linear assignment problem.
+    Parameters
+    ----------
+    distance_metric : Callable[List[Track], List[Detection], List[int], List[int]) -> ndarray
+        The distance metric is given a list of tracks and detections as well as
+        a list of N track indices and M detection indices. The metric should
+        return the NxM dimensional cost matrix, where element (i, j) is the
+        association cost between the i-th track in the given track indices and
+        the j-th detection in the given detection_indices.
+    max_distance : float
+        Gating threshold. Associations with cost larger than this value are
+        disregarded.
+    tracks : List[track.Track]
+        A list of predicted tracks at the current time step.
+    detections : List[detection.Detection]
+        A list of detections at the current time step.
+    track_indices : List[int]
+        List of track indices that maps rows in `cost_matrix` to tracks in
+        `tracks` (see description above).
+    detection_indices : List[int]
+        List of detection indices that maps columns in `cost_matrix` to
+        detections in `detections` (see description above).
+    Returns
+    -------
+    (List[(int, int)], List[int], List[int])
+        Returns a tuple with the following three entries:
+        * A list of matched track and detection indices.
+        * A list of unmatched track indices.
+        * A list of unmatched detection indices.
+    """
+    if track_indices is None:
+        track_indices = np.arange(len(tracks))
+    if detection_indices is None:
+        detection_indices = np.arange(len(detections))
+
+    if len(detection_indices) == 0 or len(track_indices) == 0:
+        return [], track_indices, detection_indices  # Nothing to match.
+
+    cost_matrix = distance_metric(tracks, detections, track_indices, detection_indices)
+    cost_matrix[cost_matrix > max_distance] = max_distance + 1e-5
+
+    row_indices, col_indices = linear_assignment(cost_matrix)
+
+    matches, unmatched_tracks, unmatched_detections = [], [], []
+    for col, detection_idx in enumerate(detection_indices):
+        if col not in col_indices:
+            unmatched_detections.append(detection_idx)
+    for row, track_idx in enumerate(track_indices):
+        if row not in row_indices:
+            unmatched_tracks.append(track_idx)
+    for row, col in zip(row_indices, col_indices):
+        track_idx = track_indices[row]
+        detection_idx = detection_indices[col]
+        if cost_matrix[row, col] > max_distance:
+            unmatched_tracks.append(track_idx)
+            unmatched_detections.append(detection_idx)
+        else:
+            matches.append((track_idx, detection_idx))
+    return matches, unmatched_tracks, unmatched_detections
+
+
+def matching_cascade(
+    distance_metric,
+    max_distance,
+    cascade_depth,
+    tracks,
+    detections,
+    track_indices=None,
+    detection_indices=None,
+):
+    """Run matching cascade.
+    Parameters
+    ----------
+    distance_metric : Callable[List[Track], List[Detection], List[int], List[int]) -> ndarray
+        The distance metric is given a list of tracks and detections as well as
+        a list of N track indices and M detection indices. The metric should
+        return the NxM dimensional cost matrix, where element (i, j) is the
+        association cost between the i-th track in the given track indices and
+        the j-th detection in the given detection indices.
+    max_distance : float
+        Gating threshold. Associations with cost larger than this value are
+        disregarded.
+    cascade_depth: int
+        The cascade depth, should be se to the maximum track age.
+    tracks : List[track.Track]
+        A list of predicted tracks at the current time step.
+    detections : List[detection.Detection]
+        A list of detections at the current time step.
+    track_indices : Optional[List[int]]
+        List of track indices that maps rows in `cost_matrix` to tracks in
+        `tracks` (see description above). Defaults to all tracks.
+    detection_indices : Optional[List[int]]
+        List of detection indices that maps columns in `cost_matrix` to
+        detections in `detections` (see description above). Defaults to all
+        detections.
+    Returns
+    -------
+    (List[(int, int)], List[int], List[int])
+        Returns a tuple with the following three entries:
+        * A list of matched track and detection indices.
+        * A list of unmatched track indices.
+        * A list of unmatched detection indices.
+    """
+    if track_indices is None:
+        track_indices = list(range(len(tracks)))
+    if detection_indices is None:
+        detection_indices = list(range(len(detections)))
+
+    unmatched_detections = detection_indices
+    matches = []
+    for level in range(cascade_depth):
+        if len(unmatched_detections) == 0:  # No detections left
+            break
+
+        track_indices_l = [k for k in track_indices if tracks[k].time_since_update == 1 + level]
+        if len(track_indices_l) == 0:  # Nothing to match at this level
+            continue
+
+        matches_l, _, unmatched_detections = min_cost_matching(
+            distance_metric,
+            max_distance,
+            tracks,
+            detections,
+            track_indices_l,
+            unmatched_detections,
+        )
+        matches += matches_l
+    unmatched_tracks = list(set(track_indices) - set(k for k, _ in matches))
+    return matches, unmatched_tracks, unmatched_detections
+
+
+def gate_cost_matrix(
+    kf,
+    cost_matrix,
+    tracks,
+    detections,
+    track_indices,
+    detection_indices,
+    gated_cost=INFTY_COST,
+    only_position=False,
+):
+    """Invalidate infeasible entries in cost matrix based on the state
+    distributions obtained by Kalman filtering.
+    Parameters
+    ----------
+    kf : The Kalman filter.
+    cost_matrix : ndarray
+        The NxM dimensional cost matrix, where N is the number of track indices
+        and M is the number of detection indices, such that entry (i, j) is the
+        association cost between `tracks[track_indices[i]]` and
+        `detections[detection_indices[j]]`.
+    tracks : List[track.Track]
+        A list of predicted tracks at the current time step.
+    detections : List[detection.Detection]
+        A list of detections at the current time step.
+    track_indices : List[int]
+        List of track indices that maps rows in `cost_matrix` to tracks in
+        `tracks` (see description above).
+    detection_indices : List[int]
+        List of detection indices that maps columns in `cost_matrix` to
+        detections in `detections` (see description above).
+    gated_cost : Optional[float]
+        Entries in the cost matrix corresponding to infeasible associations are
+        set this value. Defaults to a very large value.
+    only_position : Optional[bool]
+        If True, only the x, y position of the state distribution is considered
+        during gating. Defaults to False.
+    Returns
+    -------
+    ndarray
+        Returns the modified cost matrix.
+    """
+    gating_dim = 2 if only_position else 4
+    gating_threshold = kalman_filter.chi2inv95[gating_dim]
+    measurements = np.asarray([detections[i].to_xyah() for i in detection_indices])
+    for row, track_idx in enumerate(track_indices):
+        track = tracks[track_idx]
+        gating_distance = kf.gating_distance(track.mean, track.covariance, measurements, only_position)
+        cost_matrix[row, gating_distance > gating_threshold] = gated_cost
+    return cost_matrix
diff --git a/trackers/deepsort/reid_model.py b/trackers/deepsort/reid_model.py
new file mode 100644
index 0000000000000000000000000000000000000000..7528ed4325e2c15ae7f3154b51a0cf2ea6236e3f
--- /dev/null
+++ b/trackers/deepsort/reid_model.py
@@ -0,0 +1,141 @@
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+import numpy as np
+import cv2
+import logging
+import torchvision.transforms as transforms
+
+
+class BasicBlock(nn.Module):
+    def __init__(self, c_in, c_out, is_downsample=False):
+        super(BasicBlock, self).__init__()
+        self.is_downsample = is_downsample
+        if is_downsample:
+            self.conv1 = nn.Conv2d(c_in, c_out, 3, stride=2, padding=1, bias=False)
+        else:
+            self.conv1 = nn.Conv2d(c_in, c_out, 3, stride=1, padding=1, bias=False)
+        self.bn1 = nn.BatchNorm2d(c_out)
+        self.relu = nn.ReLU(True)
+        self.conv2 = nn.Conv2d(c_out, c_out, 3, stride=1, padding=1, bias=False)
+        self.bn2 = nn.BatchNorm2d(c_out)
+        if is_downsample:
+            self.downsample = nn.Sequential(nn.Conv2d(c_in, c_out, 1, stride=2, bias=False), nn.BatchNorm2d(c_out))
+        elif c_in != c_out:
+            self.downsample = nn.Sequential(nn.Conv2d(c_in, c_out, 1, stride=1, bias=False), nn.BatchNorm2d(c_out))
+            self.is_downsample = True
+
+    def forward(self, x):
+        y = self.conv1(x)
+        y = self.bn1(y)
+        y = self.relu(y)
+        y = self.conv2(y)
+        y = self.bn2(y)
+        if self.is_downsample:
+            x = self.downsample(x)
+        return F.relu(x.add(y), True)
+
+
+def make_layers(c_in, c_out, repeat_times, is_downsample=False):
+    blocks = []
+    for i in range(repeat_times):
+        if i == 0:
+            blocks += [
+                BasicBlock(c_in, c_out, is_downsample=is_downsample),
+            ]
+        else:
+            blocks += [
+                BasicBlock(c_out, c_out),
+            ]
+    return nn.Sequential(*blocks)
+
+
+class Net(nn.Module):
+    def __init__(self, num_classes=751, reid=False):
+        super(Net, self).__init__()
+        # 3 128 64
+        self.conv = nn.Sequential(
+            nn.Conv2d(3, 64, 3, stride=1, padding=1),
+            nn.BatchNorm2d(64),
+            nn.ReLU(inplace=True),
+            # nn.Conv2d(32,32,3,stride=1,padding=1),
+            # nn.BatchNorm2d(32),
+            # nn.ReLU(inplace=True),
+            nn.MaxPool2d(3, 2, padding=1),
+        )
+        # 32 64 32
+        self.layer1 = make_layers(64, 64, 2, False)
+        # 32 64 32
+        self.layer2 = make_layers(64, 128, 2, True)
+        # 64 32 16
+        self.layer3 = make_layers(128, 256, 2, True)
+        # 128 16 8
+        self.layer4 = make_layers(256, 512, 2, True)
+        # 256 8 4
+        self.avgpool = nn.AvgPool2d((8, 4), 1)
+        # 256 1 1
+        self.reid = reid
+        self.classifier = nn.Sequential(
+            nn.Linear(512, 256),
+            nn.BatchNorm1d(256),
+            nn.ReLU(inplace=True),
+            nn.Dropout(),
+            nn.Linear(256, num_classes),
+        )
+
+    def forward(self, x):
+        x = self.conv(x)
+        x = self.layer1(x)
+        x = self.layer2(x)
+        x = self.layer3(x)
+        x = self.layer4(x)
+        x = self.avgpool(x)
+        x = x.view(x.size(0), -1)
+        # B x 128
+        if self.reid:
+            x = x.div(x.norm(p=2, dim=1, keepdim=True))
+            return x
+        # classifier
+        x = self.classifier(x)
+        return x
+
+
+class Extractor(object):
+    def __init__(self, model_path, use_cuda=True):
+        self.net = Net(reid=True)
+        self.device = "cuda" if torch.cuda.is_available() and use_cuda else "cpu"
+        state_dict = torch.load(model_path, map_location=torch.device(self.device))["net_dict"]
+        self.net.load_state_dict(state_dict)
+        logger = logging.getLogger("root.tracker")
+        logger.info("Loading weights from {}... Done!".format(model_path))
+        self.net.to(self.device)
+        self.size = (64, 128)
+        self.norm = transforms.Compose(
+            [
+                transforms.ToTensor(),
+                transforms.Normalize([0.485, 0.456, 0.406], [0.229, 0.224, 0.225]),
+            ]
+        )
+
+    def _preprocess(self, im_crops):
+        """
+        TODO:
+            1. to float with scale from 0 to 1
+            2. resize to (64, 128) as Market1501 dataset did
+            3. concatenate to a numpy array
+            3. to torch Tensor
+            4. normalize
+        """
+
+        def _resize(im, size):
+            return cv2.resize(im.astype(np.float32) / 255.0, size)
+
+        im_batch = torch.cat([self.norm(_resize(im, self.size)).unsqueeze(0) for im in im_crops], dim=0).float()
+        return im_batch
+
+    def __call__(self, im_crops):
+        im_batch = self._preprocess(im_crops)
+        with torch.no_grad():
+            im_batch = im_batch.to(self.device)
+            features = self.net(im_batch)
+        return features.cpu().numpy()
diff --git a/trackers/deepsort/track.py b/trackers/deepsort/track.py
new file mode 100644
index 0000000000000000000000000000000000000000..baccd66a22a3d0b75915a7048fc322cc144b305e
--- /dev/null
+++ b/trackers/deepsort/track.py
@@ -0,0 +1,156 @@
+# vim: expandtab:ts=4:sw=4
+
+
+class TrackState:
+    """
+    Enumeration type for the single target track state. Newly created tracks are
+    classified as `tentative` until enough evidence has been collected. Then,
+    the track state is changed to `confirmed`. Tracks that are no longer alive
+    are classified as `deleted` to mark them for removal from the set of active
+    tracks.
+    """
+
+    Tentative = 1
+    Confirmed = 2
+    Deleted = 3
+
+
+class Track:
+    """
+    A single target track with state space `(x, y, a, h)` and associated
+    velocities, where `(x, y)` is the center of the bounding box, `a` is the
+    aspect ratio and `h` is the height.
+    Parameters
+    ----------
+    mean : ndarray
+        Mean vector of the initial state distribution.
+    covariance : ndarray
+        Covariance matrix of the initial state distribution.
+    track_id : int
+        A unique track identifier.
+    n_init : int
+        Number of consecutive detections before the track is confirmed. The
+        track state is set to `Deleted` if a miss occurs within the first
+        `n_init` frames.
+    max_age : int
+        The maximum number of consecutive misses before the track state is
+        set to `Deleted`.
+    feature : Optional[ndarray]
+        Feature vector of the detection this track originates from. If not None,
+        this feature is added to the `features` cache.
+    Attributes
+    ----------
+    mean : ndarray
+        Mean vector of the initial state distribution.
+    covariance : ndarray
+        Covariance matrix of the initial state distribution.
+    track_id : int
+        A unique track identifier.
+    hits : int
+        Total number of measurement updates.
+    age : int
+        Total number of frames since first occurance.
+    time_since_update : int
+        Total number of frames since last measurement update.
+    state : TrackState
+        The current track state.
+    features : List[ndarray]
+        A cache of features. On each measurement update, the associated feature
+        vector is added to this list.
+    """
+
+    def __init__(self, mean, covariance, track_id, class_id, n_init, max_age, feature=None):
+        self.mean = mean
+        self.covariance = covariance
+        self.track_id = track_id
+        self.class_id = class_id
+        self.hits = 1
+        self.age = 1
+        self.time_since_update = 0
+
+        self.state = TrackState.Tentative
+        self.features = []
+        if feature is not None:
+            self.features.append(feature)
+
+        self._n_init = n_init
+        self._max_age = max_age
+        self.tlwh = None
+        self.score = 1
+
+    def to_tlwh(self):
+        """Get current position in bounding box format `(top left x, top left y,
+        width, height)`.
+        Returns
+        -------
+        ndarray
+            The bounding box.
+        """
+        ret = self.mean[:4].copy()
+        ret[2] *= ret[3]
+        ret[:2] -= ret[2:] / 2
+        return ret
+
+    def to_tlbr(self):
+        """Get current position in bounding box format `(min x, miny, max x,
+        max y)`.
+        Returns
+        -------
+        ndarray
+            The bounding box.
+        """
+        ret = self.to_tlwh()
+        ret[2:] = ret[:2] + ret[2:]
+        return ret
+
+    def increment_age(self):
+        self.age += 1
+        self.time_since_update += 1
+
+    def predict(self, kf):
+        """Propagate the state distribution to the current time step using a
+        Kalman filter prediction step.
+        Parameters
+        ----------
+        kf : kalman_filter.KalmanFilter
+            The Kalman filter.
+        """
+        self.mean, self.covariance = kf.predict(self.mean, self.covariance)
+        self.increment_age()
+
+    def update(self, kf, detection):
+        """Perform Kalman filter measurement update step and update the feature
+        cache.
+        Parameters
+        ----------
+        kf : kalman_filter.KalmanFilter
+            The Kalman filter.
+        detection : Detection
+            The associated detection.
+        """
+        self.mean, self.covariance = kf.update(self.mean, self.covariance, detection.to_xyah())
+        self.features.append(detection.feature)
+
+        self.hits += 1
+        self.time_since_update = 0
+        if self.state == TrackState.Tentative and self.hits >= self._n_init:
+            self.state = TrackState.Confirmed
+
+    def mark_missed(self):
+        """Mark this track as missed (no association at the current time step)."""
+        if self.state == TrackState.Tentative:
+            self.state = TrackState.Deleted
+        elif self.time_since_update > self._max_age:
+            self.state = TrackState.Deleted
+
+    def is_tentative(self):
+        """Returns True if this track is tentative (unconfirmed)."""
+        return self.state == TrackState.Tentative
+
+    def is_confirmed(self):
+        """Returns True if this track is confirmed."""
+        return self.state == TrackState.Confirmed
+
+    def is_deleted(self):
+        """Returns True if this track is dead and should be deleted."""
+        return self.state == TrackState.Deleted
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diff --git a/trackers/fairmot/__pycache__/utils.cpython-37.pyc b/trackers/fairmot/__pycache__/utils.cpython-37.pyc
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diff --git a/trackers/fairmot/basetrack.py b/trackers/fairmot/basetrack.py
new file mode 100644
index 0000000000000000000000000000000000000000..10edc7e1a0dcf8a1087d30cb4782540def141293
--- /dev/null
+++ b/trackers/fairmot/basetrack.py
@@ -0,0 +1,52 @@
+import numpy as np
+from collections import OrderedDict
+
+
+class TrackState(object):
+    New = 0
+    Tracked = 1
+    Lost = 2
+    Removed = 3
+
+
+class BaseTrack(object):
+    _count = 0
+
+    track_id = 0
+    is_activated = False
+    state = TrackState.New
+
+    history = OrderedDict()
+    features = []
+    curr_feature = None
+    score = 0
+    start_frame = 0
+    frame_id = 0
+    time_since_update = 0
+
+    # multi-camera
+    location = (np.inf, np.inf)
+
+    @property
+    def end_frame(self):
+        return self.frame_id
+
+    @staticmethod
+    def next_id():
+        BaseTrack._count += 1
+        return BaseTrack._count
+
+    def activate(self, *args):
+        raise NotImplementedError
+
+    def predict(self):
+        raise NotImplementedError
+
+    def update(self, *args, **kwargs):
+        raise NotImplementedError
+
+    def mark_lost(self):
+        self.state = TrackState.Lost
+
+    def mark_removed(self):
+        self.state = TrackState.Removed
\ No newline at end of file
diff --git a/trackers/fairmot/kalman_filter.py b/trackers/fairmot/kalman_filter.py
new file mode 100644
index 0000000000000000000000000000000000000000..ab7b31e25cd9b0c46a02b06f27262ede0cb566c0
--- /dev/null
+++ b/trackers/fairmot/kalman_filter.py
@@ -0,0 +1,269 @@
+# vim: expandtab:ts=4:sw=4
+import numpy as np
+import scipy.linalg
+
+"""
+Table for the 0.95 quantile of the chi-square distribution with N degrees of
+freedom (contains values for N=1, ..., 9). Taken from MATLAB/Octave's chi2inv
+function and used as Mahalanobis gating threshold.
+"""
+chi2inv95 = {
+    1: 3.8415,
+    2: 5.9915,
+    3: 7.8147,
+    4: 9.4877,
+    5: 11.070,
+    6: 12.592,
+    7: 14.067,
+    8: 15.507,
+    9: 16.919}
+
+
+class KalmanFilter(object):
+    """
+    A simple Kalman filter for tracking bounding boxes in image space.
+
+    The 8-dimensional state space
+
+        x, y, a, h, vx, vy, va, vh
+
+    contains the bounding box center position (x, y), aspect ratio a, height h,
+    and their respective velocities.
+
+    Object motion follows a constant velocity model. The bounding box location
+    (x, y, a, h) is taken as direct observation of the state space (linear
+    observation model).
+
+    """
+
+    def __init__(self):
+        ndim, dt = 4, 1.
+
+        # Create Kalman filter model matrices.
+        self._motion_mat = np.eye(2 * ndim, 2 * ndim)
+        for i in range(ndim):
+            self._motion_mat[i, ndim + i] = dt
+        self._update_mat = np.eye(ndim, 2 * ndim)
+
+        # Motion and observation uncertainty are chosen relative to the current
+        # state estimate. These weights control the amount of uncertainty in
+        # the model. This is a bit hacky.
+        self._std_weight_position = 1. / 20
+        self._std_weight_velocity = 1. / 160
+
+    def initiate(self, measurement):
+        """Create track from unassociated measurement.
+
+        Parameters
+        ----------
+        measurement : ndarray
+            Bounding box coordinates (x, y, a, h) with center position (x, y),
+            aspect ratio a, and height h.
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector (8 dimensional) and covariance matrix (8x8
+            dimensional) of the new track. Unobserved velocities are initialized
+            to 0 mean.
+
+        """
+        mean_pos = measurement
+        mean_vel = np.zeros_like(mean_pos)
+        mean = np.r_[mean_pos, mean_vel]
+
+        std = [
+            2 * self._std_weight_position * measurement[3],
+            2 * self._std_weight_position * measurement[3],
+            1e-2,
+            2 * self._std_weight_position * measurement[3],
+            10 * self._std_weight_velocity * measurement[3],
+            10 * self._std_weight_velocity * measurement[3],
+            1e-5,
+            10 * self._std_weight_velocity * measurement[3]]
+        covariance = np.diag(np.square(std))
+        return mean, covariance
+
+    def predict(self, mean, covariance):
+        """Run Kalman filter prediction step.
+
+        Parameters
+        ----------
+        mean : ndarray
+            The 8 dimensional mean vector of the object state at the previous
+            time step.
+        covariance : ndarray
+            The 8x8 dimensional covariance matrix of the object state at the
+            previous time step.
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector and covariance matrix of the predicted
+            state. Unobserved velocities are initialized to 0 mean.
+
+        """
+        std_pos = [
+            self._std_weight_position * mean[3],
+            self._std_weight_position * mean[3],
+            1e-2,
+            self._std_weight_position * mean[3]]
+        std_vel = [
+            self._std_weight_velocity * mean[3],
+            self._std_weight_velocity * mean[3],
+            1e-5,
+            self._std_weight_velocity * mean[3]]
+        motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))
+
+        #mean = np.dot(self._motion_mat, mean)
+        mean = np.dot(mean, self._motion_mat.T)
+        covariance = np.linalg.multi_dot((
+            self._motion_mat, covariance, self._motion_mat.T)) + motion_cov
+
+        return mean, covariance
+
+    def project(self, mean, covariance):
+        """Project state distribution to measurement space.
+
+        Parameters
+        ----------
+        mean : ndarray
+            The state's mean vector (8 dimensional array).
+        covariance : ndarray
+            The state's covariance matrix (8x8 dimensional).
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the projected mean and covariance matrix of the given state
+            estimate.
+
+        """
+        std = [
+            self._std_weight_position * mean[3],
+            self._std_weight_position * mean[3],
+            1e-1,
+            self._std_weight_position * mean[3]]
+        innovation_cov = np.diag(np.square(std))
+
+        mean = np.dot(self._update_mat, mean)
+        covariance = np.linalg.multi_dot((
+            self._update_mat, covariance, self._update_mat.T))
+        return mean, covariance + innovation_cov
+
+    def multi_predict(self, mean, covariance):
+        """Run Kalman filter prediction step (Vectorized version).
+        Parameters
+        ----------
+        mean : ndarray
+            The Nx8 dimensional mean matrix of the object states at the previous
+            time step.
+        covariance : ndarray
+            The Nx8x8 dimensional covariance matrics of the object states at the
+            previous time step.
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector and covariance matrix of the predicted
+            state. Unobserved velocities are initialized to 0 mean.
+        """
+        std_pos = [
+            self._std_weight_position * mean[:, 3],
+            self._std_weight_position * mean[:, 3],
+            1e-2 * np.ones_like(mean[:, 3]),
+            self._std_weight_position * mean[:, 3]]
+        std_vel = [
+            self._std_weight_velocity * mean[:, 3],
+            self._std_weight_velocity * mean[:, 3],
+            1e-5 * np.ones_like(mean[:, 3]),
+            self._std_weight_velocity * mean[:, 3]]
+        sqr = np.square(np.r_[std_pos, std_vel]).T
+
+        motion_cov = []
+        for i in range(len(mean)):
+            motion_cov.append(np.diag(sqr[i]))
+        motion_cov = np.asarray(motion_cov)
+
+        mean = np.dot(mean, self._motion_mat.T)
+        left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
+        covariance = np.dot(left, self._motion_mat.T) + motion_cov
+
+        return mean, covariance
+
+    def update(self, mean, covariance, measurement):
+        """Run Kalman filter correction step.
+
+        Parameters
+        ----------
+        mean : ndarray
+            The predicted state's mean vector (8 dimensional).
+        covariance : ndarray
+            The state's covariance matrix (8x8 dimensional).
+        measurement : ndarray
+            The 4 dimensional measurement vector (x, y, a, h), where (x, y)
+            is the center position, a the aspect ratio, and h the height of the
+            bounding box.
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the measurement-corrected state distribution.
+
+        """
+        projected_mean, projected_cov = self.project(mean, covariance)
+
+        chol_factor, lower = scipy.linalg.cho_factor(
+            projected_cov, lower=True, check_finite=False)
+        kalman_gain = scipy.linalg.cho_solve(
+            (chol_factor, lower), np.dot(covariance, self._update_mat.T).T,
+            check_finite=False).T
+        innovation = measurement - projected_mean
+
+        new_mean = mean + np.dot(innovation, kalman_gain.T)
+        new_covariance = covariance - np.linalg.multi_dot((
+            kalman_gain, projected_cov, kalman_gain.T))
+        return new_mean, new_covariance
+
+    def gating_distance(self, mean, covariance, measurements,
+                        only_position=False, metric='maha'):
+        """Compute gating distance between state distribution and measurements.
+        A suitable distance threshold can be obtained from `chi2inv95`. If
+        `only_position` is False, the chi-square distribution has 4 degrees of
+        freedom, otherwise 2.
+        Parameters
+        ----------
+        mean : ndarray
+            Mean vector over the state distribution (8 dimensional).
+        covariance : ndarray
+            Covariance of the state distribution (8x8 dimensional).
+        measurements : ndarray
+            An Nx4 dimensional matrix of N measurements, each in
+            format (x, y, a, h) where (x, y) is the bounding box center
+            position, a the aspect ratio, and h the height.
+        only_position : Optional[bool]
+            If True, distance computation is done with respect to the bounding
+            box center position only.
+        Returns
+        -------
+        ndarray
+            Returns an array of length N, where the i-th element contains the
+            squared Mahalanobis distance between (mean, covariance) and
+            `measurements[i]`.
+        """
+        mean, covariance = self.project(mean, covariance)
+        if only_position:
+            mean, covariance = mean[:2], covariance[:2, :2]
+            measurements = measurements[:, :2]
+
+        d = measurements - mean
+        if metric == 'gaussian':
+            return np.sum(d * d, axis=1)
+        elif metric == 'maha':
+            cholesky_factor = np.linalg.cholesky(covariance)
+            z = scipy.linalg.solve_triangular(
+                cholesky_factor, d.T, lower=True, check_finite=False,
+                overwrite_b=True)
+            squared_maha = np.sum(z * z, axis=0)
+            return squared_maha
+        else:
+            raise ValueError('invalid distance metric')
diff --git a/trackers/fairmot/matching.py b/trackers/fairmot/matching.py
new file mode 100644
index 0000000000000000000000000000000000000000..27e465aad340e78feb5f055cc2c161389dd56a24
--- /dev/null
+++ b/trackers/fairmot/matching.py
@@ -0,0 +1,136 @@
+import cv2
+import numpy as np
+import scipy
+import lap
+from scipy.spatial.distance import cdist
+
+from cython_bbox import bbox_overlaps as bbox_ious
+from . import kalman_filter
+import time
+
+def merge_matches(m1, m2, shape):
+    O,P,Q = shape
+    m1 = np.asarray(m1)
+    m2 = np.asarray(m2)
+
+    M1 = scipy.sparse.coo_matrix((np.ones(len(m1)), (m1[:, 0], m1[:, 1])), shape=(O, P))
+    M2 = scipy.sparse.coo_matrix((np.ones(len(m2)), (m2[:, 0], m2[:, 1])), shape=(P, Q))
+
+    mask = M1*M2
+    match = mask.nonzero()
+    match = list(zip(match[0], match[1]))
+    unmatched_O = tuple(set(range(O)) - set([i for i, j in match]))
+    unmatched_Q = tuple(set(range(Q)) - set([j for i, j in match]))
+
+    return match, unmatched_O, unmatched_Q
+
+
+def _indices_to_matches(cost_matrix, indices, thresh):
+    matched_cost = cost_matrix[tuple(zip(*indices))]
+    matched_mask = (matched_cost <= thresh)
+
+    matches = indices[matched_mask]
+    unmatched_a = tuple(set(range(cost_matrix.shape[0])) - set(matches[:, 0]))
+    unmatched_b = tuple(set(range(cost_matrix.shape[1])) - set(matches[:, 1]))
+
+    return matches, unmatched_a, unmatched_b
+
+
+def linear_assignment(cost_matrix, thresh):
+    if cost_matrix.size == 0:
+        return np.empty((0, 2), dtype=int), tuple(range(cost_matrix.shape[0])), tuple(range(cost_matrix.shape[1]))
+    matches, unmatched_a, unmatched_b = [], [], []
+    cost, x, y = lap.lapjv(cost_matrix, extend_cost=True, cost_limit=thresh)
+    for ix, mx in enumerate(x):
+        if mx >= 0:
+            matches.append([ix, mx])
+    unmatched_a = np.where(x < 0)[0]
+    unmatched_b = np.where(y < 0)[0]
+    matches = np.asarray(matches)
+    return matches, unmatched_a, unmatched_b
+
+
+def ious(atlbrs, btlbrs):
+    """
+    Compute cost based on IoU
+    :type atlbrs: list[tlbr] | np.ndarray
+    :type atlbrs: list[tlbr] | np.ndarray
+
+    :rtype ious np.ndarray
+    """
+    ious = np.zeros((len(atlbrs), len(btlbrs)), dtype=np.float)
+    if ious.size == 0:
+        return ious
+
+    ious = bbox_ious(
+        np.ascontiguousarray(atlbrs, dtype=np.float),
+        np.ascontiguousarray(btlbrs, dtype=np.float)
+    )
+
+    return ious
+
+
+def iou_distance(atracks, btracks):
+    """
+    Compute cost based on IoU
+    :type atracks: list[STrack]
+    :type btracks: list[STrack]
+
+    :rtype cost_matrix np.ndarray
+    """
+
+    if (len(atracks)>0 and isinstance(atracks[0], np.ndarray)) or (len(btracks) > 0 and isinstance(btracks[0], np.ndarray)):
+        atlbrs = atracks
+        btlbrs = btracks
+    else:
+        atlbrs = [track.tlbr for track in atracks]
+        btlbrs = [track.tlbr for track in btracks]
+    _ious = ious(atlbrs, btlbrs)
+    cost_matrix = 1 - _ious
+
+    return cost_matrix
+
+def embedding_distance(tracks, detections, metric='cosine'):
+    """
+    :param tracks: list[STrack]
+    :param detections: list[BaseTrack]
+    :param metric:
+    :return: cost_matrix np.ndarray
+    """
+
+    cost_matrix = np.zeros((len(tracks), len(detections)), dtype=np.float)
+    if cost_matrix.size == 0:
+        return cost_matrix
+    det_features = np.asarray([track.curr_feat for track in detections], dtype=np.float)
+    #for i, track in enumerate(tracks):
+        #cost_matrix[i, :] = np.maximum(0.0, cdist(track.smooth_feat.reshape(1,-1), det_features, metric))
+    track_features = np.asarray([track.smooth_feat for track in tracks], dtype=np.float)
+    cost_matrix = np.maximum(0.0, cdist(track_features, det_features, metric))  # Nomalized features
+    return cost_matrix
+
+
+def gate_cost_matrix(kf, cost_matrix, tracks, detections, only_position=False):
+    if cost_matrix.size == 0:
+        return cost_matrix
+    gating_dim = 2 if only_position else 4
+    gating_threshold = kalman_filter.chi2inv95[gating_dim]
+    measurements = np.asarray([det.to_xyah() for det in detections])
+    for row, track in enumerate(tracks):
+        gating_distance = kf.gating_distance(
+            track.mean, track.covariance, measurements, only_position)
+        cost_matrix[row, gating_distance > gating_threshold] = np.inf
+    return cost_matrix
+
+
+def fuse_motion(kf, cost_matrix, tracks, detections, only_position=False, lambda_=0.98):
+    if cost_matrix.size == 0:
+        return cost_matrix
+    gating_dim = 2 if only_position else 4
+    gating_threshold = kalman_filter.chi2inv95[gating_dim]
+    measurements = np.asarray([det.to_xyah() for det in detections])
+    for row, track in enumerate(tracks):
+        gating_distance = kf.gating_distance(
+            track.mean, track.covariance, measurements, only_position, metric='maha')
+        cost_matrix[row, gating_distance > gating_threshold] = np.inf
+        cost_matrix[row] = lambda_ * cost_matrix[row] + (1 - lambda_) * gating_distance
+    return cost_matrix
diff --git a/trackers/fairmot/multitracker.py b/trackers/fairmot/multitracker.py
new file mode 100644
index 0000000000000000000000000000000000000000..fafccbb523671068dbd2c0c42cde3ed05f7d58cd
--- /dev/null
+++ b/trackers/fairmot/multitracker.py
@@ -0,0 +1,347 @@
+import itertools
+import os
+import os.path as osp
+import time
+from collections import deque
+
+import cv2
+import numpy as np
+from .kalman_filter import KalmanFilter
+from tracking_utils.log import logger
+# from .utils import *
+
+from . import matching
+
+from .basetrack import BaseTrack, TrackState
+
+
+class STrack(BaseTrack):
+    shared_kalman = KalmanFilter()
+
+    def __init__(self, tlwh, score, temp_feat, buffer_size=30):
+
+        # wait activate
+        self._tlwh = np.asarray(tlwh, dtype=np.float)
+        self.kalman_filter = None
+        self.mean, self.covariance = None, None
+        self.is_activated = False
+
+        self.score = score
+        self.tracklet_len = 0
+
+        self.smooth_feat = None
+        self.update_features(temp_feat)
+        self.features = deque([], maxlen=buffer_size)
+        self.alpha = 0.9
+
+    def update_features(self, feat):
+        feat /= np.linalg.norm(feat)
+        self.curr_feat = feat
+        if self.smooth_feat is None:
+            self.smooth_feat = feat
+        else:
+            self.smooth_feat = self.alpha * self.smooth_feat + (1 - self.alpha) * feat
+        self.features.append(feat)
+        self.smooth_feat /= np.linalg.norm(self.smooth_feat)
+
+    def predict(self):
+        mean_state = self.mean.copy()
+        if self.state != TrackState.Tracked:
+            mean_state[7] = 0
+        self.mean, self.covariance = self.kalman_filter.predict(mean_state, self.covariance)
+
+    @staticmethod
+    def multi_predict(stracks):
+        if len(stracks) > 0:
+            multi_mean = np.asarray([st.mean.copy() for st in stracks])
+            multi_covariance = np.asarray([st.covariance for st in stracks])
+            for i, st in enumerate(stracks):
+                if st.state != TrackState.Tracked:
+                    multi_mean[i][7] = 0
+            multi_mean, multi_covariance = STrack.shared_kalman.multi_predict(multi_mean, multi_covariance)
+            for i, (mean, cov) in enumerate(zip(multi_mean, multi_covariance)):
+                stracks[i].mean = mean
+                stracks[i].covariance = cov
+
+    def activate(self, kalman_filter, frame_id):
+        """Start a new tracklet"""
+        self.kalman_filter = kalman_filter
+        self.track_id = self.next_id()
+        self.mean, self.covariance = self.kalman_filter.initiate(self.tlwh_to_xyah(self._tlwh))
+
+        self.tracklet_len = 0
+        self.state = TrackState.Tracked
+        if frame_id == 1:
+            self.is_activated = True
+        # self.is_activated = True
+        self.frame_id = frame_id
+        self.start_frame = frame_id
+
+    def re_activate(self, new_track, frame_id, new_id=False):
+        self.mean, self.covariance = self.kalman_filter.update(
+            self.mean, self.covariance, self.tlwh_to_xyah(new_track.tlwh)
+        )
+
+        self.update_features(new_track.curr_feat)
+        self.tracklet_len = 0
+        self.state = TrackState.Tracked
+        self.is_activated = True
+        self.frame_id = frame_id
+        if new_id:
+            self.track_id = self.next_id()
+
+    def update(self, new_track, frame_id, update_feature=True):
+        """
+        Update a matched track
+        :type new_track: STrack
+        :type frame_id: int
+        :type update_feature: bool
+        :return:
+        """
+        self.frame_id = frame_id
+        self.tracklet_len += 1
+
+        new_tlwh = new_track.tlwh
+        self.mean, self.covariance = self.kalman_filter.update(
+            self.mean, self.covariance, self.tlwh_to_xyah(new_tlwh))
+        self.state = TrackState.Tracked
+        self.is_activated = True
+
+        self.score = new_track.score
+        if update_feature:
+            self.update_features(new_track.curr_feat)
+
+    @property
+    def tlwh(self):
+        """Get current position in bounding box format `(top left x, top left y,
+                width, height)`.
+        """
+        if self.mean is None:
+            return self._tlwh.copy()
+        ret = self.mean[:4].copy()
+        ret[2] *= ret[3]
+        ret[:2] -= ret[2:] / 2
+        return ret
+
+    @property
+    def tlbr(self):
+        """Convert bounding box to format `(min x, min y, max x, max y)`, i.e.,
+        `(top left, bottom right)`.
+        """
+        ret = self.tlwh.copy()
+        ret[2:] += ret[:2]
+        return ret
+
+    @staticmethod
+    def tlwh_to_xyah(tlwh):
+        """Convert bounding box to format `(center x, center y, aspect ratio,
+        height)`, where the aspect ratio is `width / height`.
+        """
+        ret = np.asarray(tlwh).copy()
+        ret[:2] += ret[2:] / 2
+        ret[2] /= ret[3]
+        return ret
+
+    def to_xyah(self):
+        return self.tlwh_to_xyah(self.tlwh)
+
+    @staticmethod
+    def tlbr_to_tlwh(tlbr):
+        ret = np.asarray(tlbr).copy()
+        ret[2:] -= ret[:2]
+        return ret
+
+    @staticmethod
+    def tlwh_to_tlbr(tlwh):
+        ret = np.asarray(tlwh).copy()
+        ret[2:] += ret[:2]
+        return ret
+
+    def __repr__(self):
+        return 'OT_{}_({}-{})'.format(self.track_id, self.start_frame, self.end_frame)
+
+
+class JDETracker(object):
+    def __init__(self, opt, frame_rate=30):
+        self.opt = opt
+
+        self.tracked_stracks = []  # type: list[STrack]
+        self.lost_stracks = []  # type: list[STrack]
+        self.removed_stracks = []  # type: list[STrack]
+
+        self.frame_id = 0
+        self.det_thresh = opt.track_thresh
+        self.buffer_size = int(frame_rate / 30.0 * opt.track_buffer)
+        self.max_time_lost = self.buffer_size
+        self.mean = np.array([0.408, 0.447, 0.470], dtype=np.float32).reshape(1, 1, 3)
+        self.std = np.array([0.289, 0.274, 0.278], dtype=np.float32).reshape(1, 1, 3)
+
+        self.kalman_filter = KalmanFilter()
+        logger.disabled = True
+
+    def update(self, fdets, img):  # , img_info, img_size):
+        self.frame_id += 1
+        activated_starcks = []
+        refind_stracks = []
+        lost_stracks = []
+        removed_stracks = []
+        #####
+        remain_inds = fdets[:, 4] > self.opt.track_thresh
+        dets, id_feature = fdets[remain_inds, 0:5], fdets[remain_inds, 5:]
+        # vis
+        '''
+        for i in range(0, dets.shape[0]):
+            bbox = dets[i][0:4]
+            cv2.rectangle(img0, (bbox[0], bbox[1]),
+                          (bbox[2], bbox[3]),
+                          (0, 255, 0), 2)
+        cv2.imshow('dets', img0)
+        cv2.waitKey(0)
+        id0 = id0-1
+        '''
+
+        if len(dets) > 0:
+            '''Detections'''
+            detections = [STrack(STrack.tlbr_to_tlwh(tlbrs[:4]), tlbrs[4], f, 30) for
+                          (tlbrs, f) in zip(dets[:, :5], id_feature)]
+        else:
+            detections = []
+
+        ''' Add newly detected tracklets to tracked_stracks'''
+        unconfirmed = []
+        tracked_stracks = []  # type: list[STrack]
+        for track in self.tracked_stracks:
+            if not track.is_activated:
+                unconfirmed.append(track)
+            else:
+                tracked_stracks.append(track)
+
+        ''' Step 2: First association, with embedding'''
+        strack_pool = joint_stracks(tracked_stracks, self.lost_stracks)
+        # Predict the current location with KF
+        # for strack in strack_pool:
+        # strack.predict()
+        STrack.multi_predict(strack_pool)
+        dists = matching.embedding_distance(strack_pool, detections)
+        # dists = matching.iou_distance(strack_pool, detections)
+        dists = matching.fuse_motion(self.kalman_filter, dists, strack_pool, detections)
+        matches, u_track, u_detection = matching.linear_assignment(dists, thresh=0.4)
+
+        for itracked, idet in matches:
+            track = strack_pool[itracked]
+            det = detections[idet]
+            if track.state == TrackState.Tracked:
+                track.update(detections[idet], self.frame_id)
+                activated_starcks.append(track)
+            else:
+                track.re_activate(det, self.frame_id, new_id=False)
+                refind_stracks.append(track)
+
+        ''' Step 3: Second association, with IOU'''
+        detections = [detections[i] for i in u_detection]
+        r_tracked_stracks = [strack_pool[i] for i in u_track if strack_pool[i].state == TrackState.Tracked]
+        dists = matching.iou_distance(r_tracked_stracks, detections)
+        matches, u_track, u_detection = matching.linear_assignment(dists, thresh=0.5)
+
+        for itracked, idet in matches:
+            track = r_tracked_stracks[itracked]
+            det = detections[idet]
+            if track.state == TrackState.Tracked:
+                track.update(det, self.frame_id)
+                activated_starcks.append(track)
+            else:
+                track.re_activate(det, self.frame_id, new_id=False)
+                refind_stracks.append(track)
+
+        for it in u_track:
+            track = r_tracked_stracks[it]
+            if not track.state == TrackState.Lost:
+                track.mark_lost()
+                lost_stracks.append(track)
+
+        '''Deal with unconfirmed tracks, usually tracks with only one beginning frame'''
+        detections = [detections[i] for i in u_detection]
+        dists = matching.iou_distance(unconfirmed, detections)
+        matches, u_unconfirmed, u_detection = matching.linear_assignment(dists, thresh=0.7)
+        for itracked, idet in matches:
+            unconfirmed[itracked].update(detections[idet], self.frame_id)
+            activated_starcks.append(unconfirmed[itracked])
+        for it in u_unconfirmed:
+            track = unconfirmed[it]
+            track.mark_removed()
+            removed_stracks.append(track)
+
+        """ Step 4: Init new stracks"""
+        for inew in u_detection:
+            track = detections[inew]
+            if track.score < self.det_thresh:
+                continue
+            track.activate(self.kalman_filter, self.frame_id)
+            activated_starcks.append(track)
+        """ Step 5: Update state"""
+        for track in self.lost_stracks:
+            if self.frame_id - track.end_frame > self.max_time_lost:
+                track.mark_removed()
+                removed_stracks.append(track)
+
+        # print('Ramained match {} s'.format(t4-t3))
+
+        self.tracked_stracks = [t for t in self.tracked_stracks if t.state == TrackState.Tracked]
+        self.tracked_stracks = joint_stracks(self.tracked_stracks, activated_starcks)
+        self.tracked_stracks = joint_stracks(self.tracked_stracks, refind_stracks)
+        self.lost_stracks = sub_stracks(self.lost_stracks, self.tracked_stracks)
+        self.lost_stracks.extend(lost_stracks)
+        self.lost_stracks = sub_stracks(self.lost_stracks, self.removed_stracks)
+        self.removed_stracks.extend(removed_stracks)
+        self.tracked_stracks, self.lost_stracks = remove_duplicate_stracks(self.tracked_stracks, self.lost_stracks)
+        # get scores of lost tracks
+        output_stracks = [track for track in self.tracked_stracks if track.is_activated]
+
+        logger.debug('===========Frame {}=========='.format(self.frame_id))
+        logger.debug('Activated: {}'.format([track.track_id for track in activated_starcks]))
+        logger.debug('Refind: {}'.format([track.track_id for track in refind_stracks]))
+        logger.debug('Lost: {}'.format([track.track_id for track in lost_stracks]))
+        logger.debug('Removed: {}'.format([track.track_id for track in removed_stracks]))
+
+        return output_stracks
+
+
+def joint_stracks(tlista, tlistb):
+    exists = {}
+    res = []
+    for t in tlista:
+        exists[t.track_id] = 1
+        res.append(t)
+    for t in tlistb:
+        tid = t.track_id
+        if not exists.get(tid, 0):
+            exists[tid] = 1
+            res.append(t)
+    return res
+
+
+def sub_stracks(tlista, tlistb):
+    stracks = {}
+    for t in tlista:
+        stracks[t.track_id] = t
+    for t in tlistb:
+        tid = t.track_id
+        if stracks.get(tid, 0):
+            del stracks[tid]
+    return list(stracks.values())
+
+
+def remove_duplicate_stracks(stracksa, stracksb):
+    pdist = matching.iou_distance(stracksa, stracksb)
+    pairs = np.where(pdist < 0.15)
+    dupa, dupb = list(), list()
+    for p, q in zip(*pairs):
+        timep = stracksa[p].frame_id - stracksa[p].start_frame
+        timeq = stracksb[q].frame_id - stracksb[q].start_frame
+        if timep > timeq:
+            dupb.append(q)
+        else:
+            dupa.append(p)
+    resa = [t for i, t in enumerate(stracksa) if not i in dupa]
+    resb = [t for i, t in enumerate(stracksb) if not i in dupb]
+    return resa, resb
diff --git a/trackers/fairmot/utils.py b/trackers/fairmot/utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..cbfba7e400bc92631b51bf01d41e868e1b7c6b89
--- /dev/null
+++ b/trackers/fairmot/utils.py
@@ -0,0 +1,433 @@
+import glob
+import random
+import time
+import os
+import os.path as osp
+
+import cv2
+import matplotlib.pyplot as plt
+import numpy as np
+import torch
+import torch.nn.functional as F
+from torchvision.ops import nms
+
+#import maskrcnn_benchmark.layers.nms as nms
+# Set printoptions
+torch.set_printoptions(linewidth=1320, precision=5, profile='long')
+np.set_printoptions(linewidth=320, formatter={'float_kind': '{:11.5g}'.format})  # format short g, %precision=5
+
+def mkdir_if_missing(d):
+    if not osp.exists(d):
+        os.makedirs(d)
+
+
+def float3(x):  # format floats to 3 decimals
+    return float(format(x, '.3f'))
+
+
+def init_seeds(seed=0):
+    random.seed(seed)
+    np.random.seed(seed)
+    torch.manual_seed(seed)
+    torch.cuda.manual_seed(seed)
+    torch.cuda.manual_seed_all(seed)
+
+
+def load_classes(path):
+    """
+    Loads class labels at 'path'
+    """
+    fp = open(path, 'r')
+    names = fp.read().split('\n')
+    return list(filter(None, names))  # filter removes empty strings (such as last line)
+
+
+def model_info(model):  # Plots a line-by-line description of a PyTorch model
+    n_p = sum(x.numel() for x in model.parameters())  # number parameters
+    n_g = sum(x.numel() for x in model.parameters() if x.requires_grad)  # number gradients
+    print('\n%5s %50s %9s %12s %20s %12s %12s' % ('layer', 'name', 'gradient', 'parameters', 'shape', 'mu', 'sigma'))
+    for i, (name, p) in enumerate(model.named_parameters()):
+        name = name.replace('module_list.', '')
+        print('%5g %50s %9s %12g %20s %12.3g %12.3g' % (
+            i, name, p.requires_grad, p.numel(), list(p.shape), p.mean(), p.std()))
+    print('Model Summary: %g layers, %g parameters, %g gradients\n' % (i + 1, n_p, n_g))
+
+
+
+def plot_one_box(x, img, color=None, label=None, line_thickness=None):  # Plots one bounding box on image img
+    tl = line_thickness or round(0.0004 * max(img.shape[0:2])) + 1  # line thickness
+    color = color or [random.randint(0, 255) for _ in range(3)]
+    c1, c2 = (int(x[0]), int(x[1])), (int(x[2]), int(x[3]))
+    cv2.rectangle(img, c1, c2, color, thickness=tl)
+    if label:
+        tf = max(tl - 1, 1)  # font thickness
+        t_size = cv2.getTextSize(label, 0, fontScale=tl / 3, thickness=tf)[0]
+        c2 = c1[0] + t_size[0], c1[1] - t_size[1] - 3
+        cv2.rectangle(img, c1, c2, color, -1)  # filled
+        cv2.putText(img, label, (c1[0], c1[1] - 2), 0, tl / 3, [225, 255, 255], thickness=tf, lineType=cv2.LINE_AA)
+
+
+def weights_init_normal(m):
+    classname = m.__class__.__name__
+    if classname.find('Conv') != -1:
+        torch.nn.init.normal_(m.weight.data, 0.0, 0.03)
+    elif classname.find('BatchNorm2d') != -1:
+        torch.nn.init.normal_(m.weight.data, 1.0, 0.03)
+        torch.nn.init.constant_(m.bias.data, 0.0)
+
+
+def xyxy2xywh(x):
+    # Convert bounding box format from [x1, y1, x2, y2] to [x, y, w, h]
+    y = torch.zeros(x.shape) if x.dtype is torch.float32 else np.zeros(x.shape)
+    y[:, 0] = (x[:, 0] + x[:, 2]) / 2
+    y[:, 1] = (x[:, 1] + x[:, 3]) / 2
+    y[:, 2] = x[:, 2] - x[:, 0]
+    y[:, 3] = x[:, 3] - x[:, 1]
+    return y
+
+
+def xywh2xyxy(x):
+    # Convert bounding box format from [x, y, w, h] to [x1, y1, x2, y2]
+    y = torch.zeros(x.shape) if x.dtype is torch.float32 else np.zeros(x.shape)
+    y[:, 0] = (x[:, 0] - x[:, 2] / 2)
+    y[:, 1] = (x[:, 1] - x[:, 3] / 2)
+    y[:, 2] = (x[:, 0] + x[:, 2] / 2)
+    y[:, 3] = (x[:, 1] + x[:, 3] / 2)
+    return y
+
+
+def scale_coords(img_size, coords, img0_shape):
+    # Rescale x1, y1, x2, y2 from 416 to image size
+    gain_w = float(img_size[0]) / img0_shape[1]  # gain  = old / new
+    gain_h = float(img_size[1]) / img0_shape[0]
+    gain = min(gain_w, gain_h)
+    pad_x = (img_size[0] - img0_shape[1] * gain) / 2  # width padding
+    pad_y = (img_size[1] - img0_shape[0] * gain) / 2  # height padding
+    coords[:, [0, 2]] -= pad_x
+    coords[:, [1, 3]] -= pad_y
+    coords[:, 0:4] /= gain
+    coords[:, :4] = torch.clamp(coords[:, :4], min=0)
+    return coords
+
+
+def ap_per_class(tp, conf, pred_cls, target_cls):
+    """ Compute the average precision, given the recall and precision curves.
+    Method originally from https://github.com/rafaelpadilla/Object-Detection-Metrics.
+    # Arguments
+        tp:    True positives (list).
+        conf:  Objectness value from 0-1 (list).
+        pred_cls: Predicted object classes (list).
+        target_cls: True object classes (list).
+    # Returns
+        The average precision as computed in py-faster-rcnn.
+    """
+
+    # lists/pytorch to numpy
+    tp, conf, pred_cls, target_cls = np.array(tp), np.array(conf), np.array(pred_cls), np.array(target_cls)
+
+    # Sort by objectness
+    i = np.argsort(-conf)
+    tp, conf, pred_cls = tp[i], conf[i], pred_cls[i]
+
+    # Find unique classes
+    unique_classes = np.unique(np.concatenate((pred_cls, target_cls), 0))
+
+    # Create Precision-Recall curve and compute AP for each class
+    ap, p, r = [], [], []
+    for c in unique_classes:
+        i = pred_cls == c
+        n_gt = sum(target_cls == c)  # Number of ground truth objects
+        n_p = sum(i)  # Number of predicted objects
+
+        if (n_p == 0) and (n_gt == 0):
+            continue
+        elif (n_p == 0) or (n_gt == 0):
+            ap.append(0)
+            r.append(0)
+            p.append(0)
+        else:
+            # Accumulate FPs and TPs
+            fpc = np.cumsum(1 - tp[i])
+            tpc = np.cumsum(tp[i])
+
+            # Recall
+            recall_curve = tpc / (n_gt + 1e-16)
+            r.append(tpc[-1] / (n_gt + 1e-16))
+
+            # Precision
+            precision_curve = tpc / (tpc + fpc)
+            p.append(tpc[-1] / (tpc[-1] + fpc[-1]))
+
+            # AP from recall-precision curve
+            ap.append(compute_ap(recall_curve, precision_curve))
+
+    return np.array(ap), unique_classes.astype('int32'), np.array(r), np.array(p)
+
+
+def compute_ap(recall, precision):
+    """ Compute the average precision, given the recall and precision curves.
+    Code originally from https://github.com/rbgirshick/py-faster-rcnn.
+    # Arguments
+        recall:    The recall curve (list).
+        precision: The precision curve (list).
+    # Returns
+        The average precision as computed in py-faster-rcnn.
+    """
+    # correct AP calculation
+    # first append sentinel values at the end
+
+    mrec = np.concatenate(([0.], recall, [1.]))
+    mpre = np.concatenate(([0.], precision, [0.]))
+
+    # compute the precision envelope
+    for i in range(mpre.size - 1, 0, -1):
+        mpre[i - 1] = np.maximum(mpre[i - 1], mpre[i])
+
+    # to calculate area under PR curve, look for points
+    # where X axis (recall) changes value
+    i = np.where(mrec[1:] != mrec[:-1])[0]
+
+    # and sum (\Delta recall) * prec
+    ap = np.sum((mrec[i + 1] - mrec[i]) * mpre[i + 1])
+    return ap
+
+
+def bbox_iou(box1, box2, x1y1x2y2=False):
+    """
+    Returns the IoU of two bounding boxes
+    """
+    N, M = len(box1), len(box2)
+    if x1y1x2y2:
+        # Get the coordinates of bounding boxes
+        b1_x1, b1_y1, b1_x2, b1_y2 = box1[:, 0], box1[:, 1], box1[:, 2], box1[:, 3]
+        b2_x1, b2_y1, b2_x2, b2_y2 = box2[:, 0], box2[:, 1], box2[:, 2], box2[:, 3]
+    else:
+        # Transform from center and width to exact coordinates
+        b1_x1, b1_x2 = box1[:, 0] - box1[:, 2] / 2, box1[:, 0] + box1[:, 2] / 2
+        b1_y1, b1_y2 = box1[:, 1] - box1[:, 3] / 2, box1[:, 1] + box1[:, 3] / 2
+        b2_x1, b2_x2 = box2[:, 0] - box2[:, 2] / 2, box2[:, 0] + box2[:, 2] / 2
+        b2_y1, b2_y2 = box2[:, 1] - box2[:, 3] / 2, box2[:, 1] + box2[:, 3] / 2
+
+    # get the coordinates of the intersection rectangle
+    inter_rect_x1 = torch.max(b1_x1.unsqueeze(1), b2_x1)
+    inter_rect_y1 = torch.max(b1_y1.unsqueeze(1), b2_y1)
+    inter_rect_x2 = torch.min(b1_x2.unsqueeze(1), b2_x2)
+    inter_rect_y2 = torch.min(b1_y2.unsqueeze(1), b2_y2)
+    # Intersection area
+    inter_area = torch.clamp(inter_rect_x2 - inter_rect_x1, 0) * torch.clamp(inter_rect_y2 - inter_rect_y1, 0)
+    # Union Area
+    b1_area = ((b1_x2 - b1_x1) * (b1_y2 - b1_y1))
+    b1_area = ((b1_x2 - b1_x1) * (b1_y2 - b1_y1)).view(-1,1).expand(N,M)
+    b2_area = ((b2_x2 - b2_x1) * (b2_y2 - b2_y1)).view(1,-1).expand(N,M)
+
+    return inter_area / (b1_area + b2_area - inter_area + 1e-16)
+
+
+def build_targets_max(target, anchor_wh, nA, nC, nGh, nGw):
+    """
+    returns nT, nCorrect, tx, ty, tw, th, tconf, tcls
+    """
+    nB = len(target)  # number of images in batch
+
+    txy = torch.zeros(nB, nA, nGh, nGw, 2).cuda()  # batch size, anchors, grid size
+    twh = torch.zeros(nB, nA, nGh, nGw, 2).cuda()
+    tconf = torch.LongTensor(nB, nA, nGh, nGw).fill_(0).cuda()
+    tcls = torch.ByteTensor(nB, nA, nGh, nGw, nC).fill_(0).cuda()  # nC = number of classes
+    tid = torch.LongTensor(nB, nA, nGh, nGw, 1).fill_(-1).cuda() 
+    for b in range(nB):
+        t = target[b]
+        t_id = t[:, 1].clone().long().cuda()
+        t = t[:,[0,2,3,4,5]]
+        nTb = len(t)  # number of targets
+        if nTb == 0:
+            continue
+
+        #gxy, gwh = t[:, 1:3] * nG, t[:, 3:5] * nG
+        gxy, gwh = t[: , 1:3].clone() , t[:, 3:5].clone()
+        gxy[:, 0] = gxy[:, 0] * nGw
+        gxy[:, 1] = gxy[:, 1] * nGh
+        gwh[:, 0] = gwh[:, 0] * nGw
+        gwh[:, 1] = gwh[:, 1] * nGh
+        gi = torch.clamp(gxy[:, 0], min=0, max=nGw -1).long()
+        gj = torch.clamp(gxy[:, 1], min=0, max=nGh -1).long()
+
+        # Get grid box indices and prevent overflows (i.e. 13.01 on 13 anchors)
+        #gi, gj = torch.clamp(gxy.long(), min=0, max=nG - 1).t()
+        #gi, gj = gxy.long().t()
+
+        # iou of targets-anchors (using wh only)
+        box1 = gwh
+        box2 = anchor_wh.unsqueeze(1)
+        inter_area = torch.min(box1, box2).prod(2)
+        iou = inter_area / (box1.prod(1) + box2.prod(2) - inter_area + 1e-16)
+
+        # Select best iou_pred and anchor
+        iou_best, a = iou.max(0)  # best anchor [0-2] for each target
+
+        # Select best unique target-anchor combinations
+        if nTb > 1:
+            _, iou_order = torch.sort(-iou_best)  # best to worst
+
+            # Unique anchor selection
+            u = torch.stack((gi, gj, a), 0)[:, iou_order]
+            # _, first_unique = np.unique(u, axis=1, return_index=True)  # first unique indices
+            first_unique = return_torch_unique_index(u, torch.unique(u, dim=1))  # torch alternative
+            i = iou_order[first_unique]
+            # best anchor must share significant commonality (iou) with target
+            i = i[iou_best[i] > 0.60]  # TODO: examine arbitrary threshold
+            if len(i) == 0:
+                continue
+
+            a, gj, gi, t = a[i], gj[i], gi[i], t[i]
+            t_id = t_id[i]
+            if len(t.shape) == 1:
+                t = t.view(1, 5)
+        else:
+            if iou_best < 0.60:
+                continue
+        
+        tc, gxy, gwh = t[:, 0].long(), t[:, 1:3].clone(), t[:, 3:5].clone()
+        gxy[:, 0] = gxy[:, 0] * nGw
+        gxy[:, 1] = gxy[:, 1] * nGh
+        gwh[:, 0] = gwh[:, 0] * nGw
+        gwh[:, 1] = gwh[:, 1] * nGh
+
+        # XY coordinates
+        txy[b, a, gj, gi] = gxy - gxy.floor()
+
+        # Width and height
+        twh[b, a, gj, gi] = torch.log(gwh / anchor_wh[a])  # yolo method
+        # twh[b, a, gj, gi] = torch.sqrt(gwh / anchor_wh[a]) / 2 # power method
+
+        # One-hot encoding of label
+        tcls[b, a, gj, gi, tc] = 1
+        tconf[b, a, gj, gi] = 1
+        tid[b, a, gj, gi] = t_id.unsqueeze(1)
+    tbox = torch.cat([txy, twh], -1)
+    return tconf, tbox, tid
+
+
+
+
+def generate_anchor(nGh, nGw, anchor_wh):
+    nA = len(anchor_wh)
+    yy, xx =torch.meshgrid(torch.arange(nGh), torch.arange(nGw))
+    xx, yy = xx.cuda(), yy.cuda()
+
+    mesh = torch.stack([xx, yy], dim=0)                                              # Shape 2, nGh, nGw
+    mesh = mesh.unsqueeze(0).repeat(nA,1,1,1).float()                                # Shape nA x 2 x nGh x nGw
+    anchor_offset_mesh = anchor_wh.unsqueeze(-1).unsqueeze(-1).repeat(1, 1, nGh,nGw) # Shape nA x 2 x nGh x nGw
+    anchor_mesh = torch.cat([mesh, anchor_offset_mesh], dim=1)                       # Shape nA x 4 x nGh x nGw
+    return anchor_mesh
+
+def encode_delta(gt_box_list, fg_anchor_list):
+    px, py, pw, ph = fg_anchor_list[:, 0], fg_anchor_list[:,1], \
+                     fg_anchor_list[:, 2], fg_anchor_list[:,3]
+    gx, gy, gw, gh = gt_box_list[:, 0], gt_box_list[:, 1], \
+                     gt_box_list[:, 2], gt_box_list[:, 3]
+    dx = (gx - px) / pw
+    dy = (gy - py) / ph
+    dw = torch.log(gw/pw)
+    dh = torch.log(gh/ph)
+    return torch.stack([dx, dy, dw, dh], dim=1)
+
+def decode_delta(delta, fg_anchor_list):
+    px, py, pw, ph = fg_anchor_list[:, 0], fg_anchor_list[:,1], \
+                     fg_anchor_list[:, 2], fg_anchor_list[:,3]
+    dx, dy, dw, dh = delta[:, 0], delta[:, 1], delta[:, 2], delta[:, 3]
+    gx = pw * dx + px
+    gy = ph * dy + py
+    gw = pw * torch.exp(dw)
+    gh = ph * torch.exp(dh)
+    return torch.stack([gx, gy, gw, gh], dim=1)
+
+def decode_delta_map(delta_map, anchors):
+    '''
+    :param: delta_map, shape (nB, nA, nGh, nGw, 4)
+    :param: anchors, shape (nA,4)
+    '''
+    nB, nA, nGh, nGw, _ = delta_map.shape
+    anchor_mesh = generate_anchor(nGh, nGw, anchors) 
+    anchor_mesh = anchor_mesh.permute(0,2,3,1).contiguous()              # Shpae (nA x nGh x nGw) x 4
+    anchor_mesh = anchor_mesh.unsqueeze(0).repeat(nB,1,1,1,1)
+    pred_list = decode_delta(delta_map.view(-1,4), anchor_mesh.view(-1,4))
+    pred_map = pred_list.view(nB, nA, nGh, nGw, 4)
+    return pred_map
+
+
+def pooling_nms(heatmap, kernel=1):
+    pad = (kernel -1 ) // 2
+    hmax = F.max_pool2d(heatmap, (kernel, kernel), stride=1, padding=pad)
+    keep = (hmax == heatmap).float()
+    return keep * heatmap
+
+
+def non_max_suppression(prediction, conf_thres=0.5, nms_thres=0.2):
+    """
+    Removes detections with lower object confidence score than 'conf_thres'
+    Non-Maximum Suppression to further filter detections.
+    Returns detections with shape:
+        (x1, y1, x2, y2, object_conf, class_score, class_pred)
+    """
+
+    output = [None for _ in range(len(prediction))]
+    for image_i, pred in enumerate(prediction):
+        # Filter out confidence scores below threshold
+        # Get score and class with highest confidence
+
+        v = pred[:, 4] > conf_thres
+        v = v.nonzero().squeeze()
+        if len(v.shape) == 0:
+            v = v.unsqueeze(0)
+
+        pred = pred[v]
+
+        # If none are remaining => process next image
+        nP = pred.shape[0]
+        if not nP:
+            continue
+        # From (center x, center y, width, height) to (x1, y1, x2, y2)
+        pred[:, :4] = xywh2xyxy(pred[:, :4])
+        nms_indices = nms(pred[:, :4], pred[:, 4], nms_thres)
+        det_max = pred[nms_indices]        
+
+        if len(det_max) > 0:
+            # Add max detections to outputs
+            output[image_i] = det_max if output[image_i] is None else torch.cat((output[image_i], det_max))
+
+    return output
+
+
+def return_torch_unique_index(u, uv):
+    n = uv.shape[1]  # number of columns
+    first_unique = torch.zeros(n, device=u.device).long()
+    for j in range(n):
+        first_unique[j] = (uv[:, j:j + 1] == u).all(0).nonzero()[0]
+
+    return first_unique
+
+
+def strip_optimizer_from_checkpoint(filename='weights/best.pt'):
+    # Strip optimizer from *.pt files for lighter files (reduced by 2/3 size)
+
+    a = torch.load(filename, map_location='cpu')
+    a['optimizer'] = []
+    torch.save(a, filename.replace('.pt', '_lite.pt'))
+
+
+def plot_results():
+    # Plot YOLO training results file 'results.txt'
+    # import os; os.system('wget https://storage.googleapis.com/ultralytics/yolov3/results_v1.txt')
+
+    plt.figure(figsize=(14, 7))
+    s = ['X + Y', 'Width + Height', 'Confidence', 'Classification', 'Total Loss', 'mAP', 'Recall', 'Precision']
+    files = sorted(glob.glob('results*.txt'))
+    for f in files:
+        results = np.loadtxt(f, usecols=[2, 3, 4, 5, 6, 9, 10, 11]).T  # column 11 is mAP
+        x = range(1, results.shape[1])
+        for i in range(8):
+            plt.subplot(2, 4, i + 1)
+            plt.plot(x, results[i, x], marker='.', label=f)
+            plt.title(s[i])
+            if i == 0:
+                plt.legend()
diff --git a/trackers/hybrid_sort_tracker/association.py b/trackers/hybrid_sort_tracker/association.py
new file mode 100644
index 0000000000000000000000000000000000000000..9561ea98728a0818373592dbaa9a0990886ae983
--- /dev/null
+++ b/trackers/hybrid_sort_tracker/association.py
@@ -0,0 +1,800 @@
+import os
+import numpy as np
+
+def intersection_batch(bboxes1, bboxes2):
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    intersections = w * h
+    return intersections
+
+def box_area(bbox):
+    area = (bbox[2] - bbox[0]) * (bbox[3] - bbox[1])
+    return area
+
+def iou_batch(bboxes1, bboxes2):
+    """
+    From SORT: Computes IOU between two bboxes in the form [x1,y1,x2,y2]
+    """
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+    
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    o = wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])                                      
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)                                              
+    return(o)
+
+
+def cal_score_dif_batch(bboxes1, bboxes2):
+    """
+    From SORT: Computes IOU between two bboxes in the form [x1,y1,x2,y2]
+    """
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    score2 = bboxes2[..., 4]
+    score1 = bboxes1[..., 4]
+
+    return (abs(score2 - score1))
+
+def cal_score_dif_batch_two_score(bboxes1, bboxes2):
+    """
+    From SORT: Computes IOU between two bboxes in the form [x1,y1,x2,y2]
+    """
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    score2 = bboxes2[..., 5]
+    score1 = bboxes1[..., 4]
+
+    return (abs(score2 - score1))
+
+def hmiou(bboxes1, bboxes2):
+    """
+    Height_Modulated_IoU
+    """
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    yy11 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    yy12 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+
+    yy21 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    yy22 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+    o = (yy12 - yy11) / (yy22 - yy21)
+
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    o *= wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)
+    return (o)
+
+def giou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    iou = wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)  
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+    wc = xxc2 - xxc1 
+    hc = yyc2 - yyc1 
+    assert((wc > 0).all() and (hc > 0).all())
+    area_enclose = wc * hc 
+    giou = iou - (area_enclose - wh) / area_enclose
+    giou = (giou + 1.)/2.0 # resize from (-1,1) to (0,1)
+    return giou
+
+def giou_batch_true(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    union = ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)
+    iou = wh / union
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+    wc = xxc2 - xxc1
+    hc = yyc2 - yyc1
+    assert((wc > 0).all() and (hc > 0).all())
+    area_enclose = wc * hc
+    giou = iou - (area_enclose - union) / area_enclose
+    giou = (giou + 1.)/2.0 # resize from (-1,1) to (0,1)
+    return giou
+
+def diou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    # calculate the intersection box
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    iou = wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])                                      
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh) 
+
+    centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
+    centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
+    centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
+    centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
+
+    inner_diag = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+
+    outer_diag = (xxc2 - xxc1) ** 2 + (yyc2 - yyc1) ** 2
+    diou = iou - inner_diag / outer_diag
+
+    return (diou + 1) / 2.0 # resize from (-1,1) to (0,1)
+
+def ciou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    # calculate the intersection box
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    iou = wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])                                      
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh) 
+
+    centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
+    centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
+    centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
+    centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
+
+    inner_diag = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+
+    outer_diag = (xxc2 - xxc1) ** 2 + (yyc2 - yyc1) ** 2
+    
+    w1 = bboxes1[..., 2] - bboxes1[..., 0]
+    h1 = bboxes1[..., 3] - bboxes1[..., 1]
+    w2 = bboxes2[..., 2] - bboxes2[..., 0]
+    h2 = bboxes2[..., 3] - bboxes2[..., 1]
+
+    # prevent dividing over zero. add one pixel shift
+    h2 = h2 + 1.
+    h1 = h1 + 1.
+    arctan = np.arctan(w2/h2) - np.arctan(w1/h1)
+    v = (4 / (np.pi ** 2)) * (arctan ** 2)
+    S = 1 - iou 
+    alpha = v / (S+v)
+    ciou = iou - inner_diag / outer_diag - alpha * v
+    
+    return (ciou + 1) / 2.0 # resize from (-1,1) to (0,1)
+
+
+def ct_dist(bboxes1, bboxes2):
+    """
+        Measure the center distance between two sets of bounding boxes,
+        this is a coarse implementation, we don't recommend using it only
+        for association, which can be unstable and sensitive to frame rate
+        and object speed.
+    """
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
+    centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
+    centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
+    centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
+
+    ct_dist2 = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
+
+    ct_dist = np.sqrt(ct_dist2)
+
+    # The linear rescaling is a naive version and needs more study
+    ct_dist = ct_dist / ct_dist.max()
+    return ct_dist.max() - ct_dist # resize to (0,1)
+
+
+def speed_direction_batch(dets, tracks):
+    """
+    batch formulation of function 'speed_direction', compute normalized speed from batch bboxes
+    @param dets:
+    @param tracks:
+    @return: normalized speed in batch
+    """
+    tracks = tracks[..., np.newaxis]
+    CX1, CY1 = (dets[:,0] + dets[:,2])/2.0, (dets[:,1]+dets[:,3])/2.0
+    CX2, CY2 = (tracks[:,0] + tracks[:,2]) /2.0, (tracks[:,1]+tracks[:,3])/2.0
+    dx = CX1 - CX2 
+    dy = CY1 - CY2 
+    norm = np.sqrt(dx**2 + dy**2) + 1e-6
+    dx = dx / norm 
+    dy = dy / norm
+    return dy, dx # size: num_track x num_det
+
+
+def linear_assignment(cost_matrix, thresh=0.):
+    try:        # [hgx0411] goes here!
+        import lap
+        if thresh != 0:
+            _, x, y = lap.lapjv(cost_matrix, extend_cost=True, cost_limit=thresh)
+        else:
+            _, x, y = lap.lapjv(cost_matrix, extend_cost=True)
+        return np.array([[y[i], i] for i in x if i >= 0])
+    except ImportError:
+        from scipy.optimize import linear_sum_assignment
+        x, y = linear_sum_assignment(cost_matrix)
+        return np.array(list(zip(x, y)))
+
+
+def associate_detections_to_trackers(detections,trackers,iou_threshold = 0.3):
+    """
+    Assigns detections to tracked object (both represented as bounding boxes)
+    Returns 3 lists of matches, unmatched_detections and unmatched_trackers
+    """
+    if(len(trackers)==0):
+        return np.empty((0,2),dtype=int), np.arange(len(detections)), np.empty((0,5),dtype=int)
+
+    iou_matrix = iou_batch(detections, trackers)
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(-iou_matrix)
+    else:
+        matched_indices = np.empty(shape=(0,2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if(d not in matched_indices[:,0]):
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if(t not in matched_indices[:,1]):
+            unmatched_trackers.append(t)
+
+    #filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if(iou_matrix[m[0], m[1]]<iou_threshold):
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1,2))
+    if(len(matches)==0):
+        matches = np.empty((0,2),dtype=int)
+    else:
+        matches = np.concatenate(matches,axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+
+def associate(detections, trackers, iou_threshold, velocities, previous_obs, vdc_weight):    
+    if(len(trackers)==0):
+        return np.empty((0,2),dtype=int), np.arange(len(detections)), np.empty((0,5),dtype=int)
+
+    Y, X = speed_direction_batch(detections, previous_obs)
+    inertia_Y, inertia_X = velocities[:,0], velocities[:,1]
+    inertia_Y = np.repeat(inertia_Y[:, np.newaxis], Y.shape[1], axis=1)
+    inertia_X = np.repeat(inertia_X[:, np.newaxis], X.shape[1], axis=1)
+    diff_angle_cos = inertia_X * X + inertia_Y * Y
+    diff_angle_cos = np.clip(diff_angle_cos, a_min=-1, a_max=1)
+    diff_angle = np.arccos(diff_angle_cos)
+    diff_angle = (np.pi /2.0 - np.abs(diff_angle)) / np.pi
+
+    valid_mask = np.ones(previous_obs.shape[0])
+    valid_mask[np.where(previous_obs[:,4]<0)] = 0
+    
+    iou_matrix = iou_batch(detections, trackers)
+    scores = np.repeat(detections[:,-1][:, np.newaxis], trackers.shape[0], axis=1)
+    # iou_matrix = iou_matrix * scores # a trick sometiems works, we don't encourage this
+    valid_mask = np.repeat(valid_mask[:, np.newaxis], X.shape[1], axis=1)
+
+    angle_diff_cost = (valid_mask * diff_angle) * vdc_weight
+    angle_diff_cost = angle_diff_cost.T
+    angle_diff_cost = angle_diff_cost * scores
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(-(iou_matrix+angle_diff_cost))
+    else:
+        matched_indices = np.empty(shape=(0,2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if(d not in matched_indices[:,0]):
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if(t not in matched_indices[:,1]):
+            unmatched_trackers.append(t)
+
+    # filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if(iou_matrix[m[0], m[1]]<iou_threshold):
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1,2))
+    if(len(matches)==0):
+        matches = np.empty((0,2),dtype=int)
+    else:
+        matches = np.concatenate(matches,axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+
+def cost_vel(Y, X, trackers, velocities, detections, previous_obs, vdc_weight):
+    # Y, X = speed_direction_batch(detections, previous_obs)
+    inertia_Y, inertia_X = velocities[:, 0], velocities[:, 1]
+    inertia_Y = np.repeat(inertia_Y[:, np.newaxis], Y.shape[1], axis=1)
+    inertia_X = np.repeat(inertia_X[:, np.newaxis], X.shape[1], axis=1)
+    diff_angle_cos = inertia_X * X + inertia_Y * Y
+    diff_angle_cos = np.clip(diff_angle_cos, a_min=-1, a_max=1)
+    diff_angle = np.arccos(diff_angle_cos)
+    diff_angle = (np.pi / 2.0 - np.abs(diff_angle)) / np.pi
+
+    valid_mask = np.ones(previous_obs.shape[0])
+    valid_mask[np.where(previous_obs[:, 4] < 0)] = 0
+
+    # iou_matrix = iou_batch(detections, trackers)
+    scores = np.repeat(detections[:, -1][:, np.newaxis], trackers.shape[0], axis=1)
+    # iou_matrix = iou_matrix * scores # a trick sometiems works, we don't encourage this
+    valid_mask = np.repeat(valid_mask[:, np.newaxis], X.shape[1], axis=1)
+
+    angle_diff_cost = (valid_mask * diff_angle) * vdc_weight
+    angle_diff_cost = angle_diff_cost.T
+    angle_diff_cost = angle_diff_cost * scores
+    return angle_diff_cost
+
+def speed_direction_batch_lt(dets, tracks):
+    tracks = tracks[..., np.newaxis]
+    CX1, CY1 = dets[:,0], dets[:,1]
+    CX2, CY2 = tracks[:,0], tracks[:,1]
+    dx = CX1 - CX2
+    dy = CY1 - CY2
+    norm = np.sqrt(dx**2 + dy**2) + 1e-6
+    dx = dx / norm
+    dy = dy / norm
+    return dy, dx # size: num_track x num_det
+
+def speed_direction_batch_rt(dets, tracks):
+    tracks = tracks[..., np.newaxis]
+    CX1, CY1 = dets[:,0], dets[:,3]
+    CX2, CY2 = tracks[:,0], tracks[:,3]
+    dx = CX1 - CX2
+    dy = CY1 - CY2
+    norm = np.sqrt(dx**2 + dy**2) + 1e-6
+    dx = dx / norm
+    dy = dy / norm
+    return dy, dx # size: num_track x num_det
+
+def speed_direction_batch_lb(dets, tracks):
+    tracks = tracks[..., np.newaxis]
+    CX1, CY1 = dets[:,2], dets[:,1]
+    CX2, CY2 = tracks[:,2], tracks[:,1]
+    dx = CX1 - CX2
+    dy = CY1 - CY2
+    norm = np.sqrt(dx**2 + dy**2) + 1e-6
+    dx = dx / norm
+    dy = dy / norm
+    return dy, dx # size: num_track x num_det
+
+def speed_direction_batch_rb(dets, tracks):
+    tracks = tracks[..., np.newaxis]
+    CX1, CY1 = dets[:,2], dets[:,3]
+    CX2, CY2 = tracks[:,2], tracks[:,3]
+    dx = CX1 - CX2
+    dy = CY1 - CY2
+    norm = np.sqrt(dx**2 + dy**2) + 1e-6
+    dx = dx / norm
+    dy = dy / norm
+    return dy, dx # size: num_track x num_det
+
+def associate_4_points(detections, trackers, iou_threshold, lt, rt, lb, rb, previous_obs, vdc_weight, iou_type=None, args=None):
+    if (len(trackers) == 0):
+        return np.empty((0, 2), dtype=int), np.arange(len(detections)), np.empty((0, 5), dtype=int)
+
+    Y1, X1 = speed_direction_batch_lt(detections, previous_obs)
+    Y2, X2 = speed_direction_batch_rt(detections, previous_obs)
+    Y3, X3 = speed_direction_batch_lb(detections, previous_obs)
+    Y4, X4 = speed_direction_batch_rb(detections, previous_obs)
+    YC, XC = speed_direction_batch(detections, previous_obs)
+    cost_lt = cost_vel(Y1, X1, trackers, lt, detections, previous_obs, vdc_weight)
+    cost_rt = cost_vel(Y2, X2, trackers, rt, detections, previous_obs, vdc_weight)
+    cost_lb = cost_vel(Y3, X3, trackers, lb, detections, previous_obs, vdc_weight)
+    cost_rb = cost_vel(Y4, X4, trackers, rb, detections, previous_obs, vdc_weight)
+
+    iou_matrix = iou_type(detections, trackers)
+    angle_diff_cost = cost_lt + cost_rt + cost_lb + cost_rb
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(-(iou_matrix + angle_diff_cost))
+    else:
+        matched_indices = np.empty(shape=(0, 2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if (d not in matched_indices[:, 0]):
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if (t not in matched_indices[:, 1]):
+            unmatched_trackers.append(t)
+
+    # filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if (iou_matrix[m[0], m[1]] < iou_threshold):
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1, 2))
+    if (len(matches) == 0):
+        matches = np.empty((0, 2), dtype=int)
+    else:
+        matches = np.concatenate(matches, axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+def associate_4_points_with_score(detections, trackers, iou_threshold, lt, rt, lb, rb, previous_obs, vdc_weight, iou_type=None, args=None):
+    if (len(trackers) == 0):
+        return np.empty((0, 2), dtype=int), np.arange(len(detections)), np.empty((0, 5), dtype=int)
+
+    Y1, X1 = speed_direction_batch_lt(detections, previous_obs)
+    Y2, X2 = speed_direction_batch_rt(detections, previous_obs)
+    Y3, X3 = speed_direction_batch_lb(detections, previous_obs)
+    Y4, X4 = speed_direction_batch_rb(detections, previous_obs)
+    cost_lt = cost_vel(Y1, X1, trackers, lt, detections, previous_obs, vdc_weight)
+    cost_rt = cost_vel(Y2, X2, trackers, rt, detections, previous_obs, vdc_weight)
+    cost_lb = cost_vel(Y3, X3, trackers, lb, detections, previous_obs, vdc_weight)
+    cost_rb = cost_vel(Y4, X4, trackers, rb, detections, previous_obs, vdc_weight)
+    iou_matrix = iou_type(detections, trackers)
+    score_dif = cal_score_dif_batch(detections, trackers)
+
+    angle_diff_cost = cost_lt + cost_rt + cost_lb + cost_rb
+
+    # TCM
+    angle_diff_cost -= score_dif * args.TCM_first_step_weight
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(-(iou_matrix + angle_diff_cost))
+    else:
+        matched_indices = np.empty(shape=(0, 2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if (d not in matched_indices[:, 0]):
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if (t not in matched_indices[:, 1]):
+            unmatched_trackers.append(t)
+
+    # filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if (iou_matrix[m[0], m[1]] < iou_threshold):
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1, 2))
+    if (len(matches) == 0):
+        matches = np.empty((0, 2), dtype=int)
+    else:
+        matches = np.concatenate(matches, axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+def associate_4_points_with_score_with_reid(detections, trackers, iou_threshold, lt, rt, lb, rb, previous_obs, vdc_weight,
+                                            iou_type=None, args=None,emb_cost=None, weights=(1.0, 0), thresh=0.8,
+                                            long_emb_dists=None, with_longterm_reid=False,
+                                            longterm_reid_weight=0.0, with_longterm_reid_correction=False,
+                                            longterm_reid_correction_thresh=0.0, dataset="dancetrack"):
+    if (len(trackers) == 0):
+        return np.empty((0, 2), dtype=int), np.arange(len(detections)), np.empty((0, 5), dtype=int)
+
+    Y1, X1 = speed_direction_batch_lt(detections, previous_obs)
+    Y2, X2 = speed_direction_batch_rt(detections, previous_obs)
+    Y3, X3 = speed_direction_batch_lb(detections, previous_obs)
+    Y4, X4 = speed_direction_batch_rb(detections, previous_obs)
+    cost_lt = cost_vel(Y1, X1, trackers, lt, detections, previous_obs, vdc_weight)
+    cost_rt = cost_vel(Y2, X2, trackers, rt, detections, previous_obs, vdc_weight)
+    cost_lb = cost_vel(Y3, X3, trackers, lb, detections, previous_obs, vdc_weight)
+    cost_rb = cost_vel(Y4, X4, trackers, rb, detections, previous_obs, vdc_weight)
+    iou_matrix = iou_type(detections, trackers)
+    score_dif = cal_score_dif_batch(detections, trackers)
+
+    angle_diff_cost = cost_lt + cost_rt + cost_lb + cost_rb
+
+    # TCM
+    angle_diff_cost -= score_dif * args.TCM_first_step_weight
+
+    if min(iou_matrix.shape) > 0:
+        if emb_cost is None:
+            a = (iou_matrix > iou_threshold).astype(np.int32)
+            if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+                matched_indices = np.stack(np.where(a), axis=1)
+            else:
+                matched_indices = linear_assignment(-(iou_matrix + angle_diff_cost))
+        else:
+            if not with_longterm_reid:
+                matched_indices = linear_assignment(weights[0] * (-(iou_matrix + angle_diff_cost)) + weights[1] * emb_cost) # , thresh=thresh
+            else:   # long-term reid feats
+                matched_indices = linear_assignment(weights[0] * (-(iou_matrix + angle_diff_cost)) +
+                                                    weights[1] * emb_cost + longterm_reid_weight * long_emb_dists)  # , thresh=thresh
+
+        if matched_indices.size == 0:
+            matched_indices = np.empty(shape=(0, 2))
+    else:
+        matched_indices = np.empty(shape=(0, 2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if (d not in matched_indices[:, 0]):
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if (t not in matched_indices[:, 1]):
+            unmatched_trackers.append(t)
+
+    # filter out matched with low IOU (and long-term ReID feats)
+    matches = []
+    # iou_matrix_thre = iou_matrix if dataset == "dancetrack" else iou_matrix - score_dif
+    iou_matrix_thre = iou_matrix - score_dif
+    if with_longterm_reid_correction:
+        for m in matched_indices:
+            if (emb_cost[m[0], m[1]] > longterm_reid_correction_thresh) and (iou_matrix_thre[m[0], m[1]] < iou_threshold):
+                print("correction:", emb_cost[m[0], m[1]])
+                unmatched_detections.append(m[0])
+                unmatched_trackers.append(m[1])
+            else:
+                matches.append(m.reshape(1, 2))
+    else:
+        for m in matched_indices:
+            if (iou_matrix_thre[m[0], m[1]] < iou_threshold):
+                unmatched_detections.append(m[0])
+                unmatched_trackers.append(m[1])
+            else:
+                matches.append(m.reshape(1, 2))
+
+    if (len(matches) == 0):
+        matches = np.empty((0, 2), dtype=int)
+    else:
+        matches = np.concatenate(matches, axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+
+def associate_kitti(detections, trackers, det_cates, iou_threshold, 
+        velocities, previous_obs, vdc_weight):
+    if(len(trackers)==0):
+        return np.empty((0,2),dtype=int), np.arange(len(detections)), np.empty((0,5),dtype=int)
+
+    """
+        Cost from the velocity direction consistency
+    """
+    Y, X = speed_direction_batch(detections, previous_obs)
+    inertia_Y, inertia_X = velocities[:,0], velocities[:,1]
+    inertia_Y = np.repeat(inertia_Y[:, np.newaxis], Y.shape[1], axis=1)
+    inertia_X = np.repeat(inertia_X[:, np.newaxis], X.shape[1], axis=1)
+    diff_angle_cos = inertia_X * X + inertia_Y * Y
+    diff_angle_cos = np.clip(diff_angle_cos, a_min=-1, a_max=1)
+    diff_angle = np.arccos(diff_angle_cos)
+    diff_angle = (np.pi /2.0 - np.abs(diff_angle)) / np.pi
+
+    valid_mask = np.ones(previous_obs.shape[0])
+    valid_mask[np.where(previous_obs[:,4]<0)]=0  
+    valid_mask = np.repeat(valid_mask[:, np.newaxis], X.shape[1], axis=1)
+
+    scores = np.repeat(detections[:,-1][:, np.newaxis], trackers.shape[0], axis=1)
+    angle_diff_cost = (valid_mask * diff_angle) * vdc_weight
+    angle_diff_cost = angle_diff_cost.T
+    angle_diff_cost = angle_diff_cost * scores
+
+    """
+        Cost from IoU
+    """
+    iou_matrix = iou_batch(detections, trackers)
+    
+
+    """
+        With multiple categories, generate the cost for catgory mismatch
+    """
+    num_dets = detections.shape[0]
+    num_trk = trackers.shape[0]
+    cate_matrix = np.zeros((num_dets, num_trk))
+    for i in range(num_dets):
+            for j in range(num_trk):
+                if det_cates[i] != trackers[j, 4]:
+                        cate_matrix[i][j] = -1e6
+    
+    cost_matrix = - iou_matrix -angle_diff_cost - cate_matrix
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(cost_matrix)
+    else:
+        matched_indices = np.empty(shape=(0,2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if(d not in matched_indices[:,0]):
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if(t not in matched_indices[:,1]):
+            unmatched_trackers.append(t)
+
+    #filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if(iou_matrix[m[0], m[1]]<iou_threshold):
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1,2))
+    if(len(matches)==0):
+        matches = np.empty((0,2),dtype=int)
+    else:
+        matches = np.concatenate(matches,axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+# compute embedding distance and gating, borrowed and modified from FairMOT
+from scipy.spatial.distance import cdist
+def embedding_distance(tracks_feat, detections_feat, metric='cosine'):
+    """
+    :param tracks: list[KalmanBoxTracker]
+    :param detections: list[KalmanBoxTracker]
+    :param metric:
+    :return: cost_matrix np.ndarray
+    """
+
+    cost_matrix = np.zeros((len(tracks_feat), len(detections_feat)), dtype=np.float)
+    if cost_matrix.size == 0:
+        return cost_matrix
+    # det_features = np.asarray([track.curr_feat for track in detections], dtype=np.float)    # [detection_num, emd_dim]
+    # #for i, track in enumerate(tracks):
+    #     #cost_matrix[i, :] = np.maximum(0.0, cdist(track.smooth_feat.reshape(1,-1), det_features, metric))
+    # track_features = np.asarray([track.smooth_feat for track in tracks], dtype=np.float)    # [track_num, emd_dim]
+    cost_matrix = np.maximum(0.0, cdist(tracks_feat, detections_feat, metric))  # Nomalized features, metric: cosine, [track_num, detection_num]
+    return cost_matrix
+
+chi2inv95 = {
+    1: 3.8415,
+    2: 5.9915,
+    3: 7.8147,
+    4: 9.4877,
+    5: 11.070,
+    6: 12.592,
+    7: 14.067,
+    8: 15.507,
+    9: 16.919}
+
+# [hgx0411] compute embedding distance and gating, borrowed and modified from FairMOT
+def fuse_motion(cost_matrix, tracks, detections, only_position=False, lambda_=0.98):
+    if cost_matrix.size == 0:
+        return cost_matrix
+    gating_dim = 2 if only_position else 4
+    gating_threshold = chi2inv95[gating_dim]
+    for row, track in enumerate(tracks):
+        gating_distance = track.kf.gating_distance(detections, only_position, metric='maha')
+        cost_matrix[row, gating_distance > gating_threshold] = np.inf
+        cost_matrix[row] = lambda_ * cost_matrix[row] + (1 - lambda_) * gating_distance
+    return cost_matrix
+
+# [hgx0411] compute embedding distance and gating, borrowed and modified from FairMOT
+import lap
+def linear_assignment_appearance(cost_matrix, thresh):
+    if cost_matrix.size == 0:
+        return np.empty((0, 2), dtype=int), tuple(range(cost_matrix.shape[0])), tuple(range(cost_matrix.shape[1]))
+    matches, unmatched_a, unmatched_b = [], [], []
+    cost, x, y = lap.lapjv(cost_matrix, extend_cost=True, cost_limit=thresh)
+    for ix, mx in enumerate(x):
+        if mx >= 0:
+            matches.append([ix, mx])
+    unmatched_a = np.where(x < 0)[0]
+    unmatched_b = np.where(y < 0)[0]
+    matches = np.asarray(matches)
+    return matches, unmatched_a, unmatched_b
+
+def fuse_score(cost_matrix, det_scores):
+    if cost_matrix.size == 0:
+        return cost_matrix
+    iou_sim = - cost_matrix
+    det_scores = np.expand_dims(det_scores, axis=1).repeat(cost_matrix.shape[1], axis=1)
+    fuse_sim = iou_sim * det_scores
+    fuse_cost = - fuse_sim
+    return fuse_cost
\ No newline at end of file
diff --git a/trackers/hybrid_sort_tracker/hybrid_sort.py b/trackers/hybrid_sort_tracker/hybrid_sort.py
new file mode 100644
index 0000000000000000000000000000000000000000..f2a6dc9d4b2285e40a8197e667d87b5629c1efd8
--- /dev/null
+++ b/trackers/hybrid_sort_tracker/hybrid_sort.py
@@ -0,0 +1,561 @@
+"""
+    This script is adopted from the SORT script by Alex Bewley alex@bewley.ai
+"""
+from __future__ import print_function
+
+import numpy as np
+from .association import *
+
+
+def k_previous_obs(observations, cur_age, k):
+    if len(observations) == 0:
+        return [-1, -1, -1, -1, -1]
+    for i in range(k):
+        dt = k - i
+        if cur_age - dt in observations:
+            return observations[cur_age-dt]
+    max_age = max(observations.keys())
+    return observations[max_age]
+
+
+def convert_bbox_to_z(bbox):
+    """
+    Takes a bounding box in the form [x1,y1,x2,y2] and returns z in the form
+      [x,y,s,r] where x,y is the centre of the box and s is the scale/area and r is
+      the aspect ratio
+    """
+    w = bbox[2] - bbox[0]
+    h = bbox[3] - bbox[1]
+    x = bbox[0] + w/2.
+    y = bbox[1] + h/2.
+    s = w * h  # scale is just area
+    r = w / float(h+1e-6)
+    score = bbox[4]
+    if score:
+        return np.array([x, y, s, score, r]).reshape((5, 1))
+    else:
+        return np.array([x, y, s, r]).reshape((4, 1))
+
+
+def convert_x_to_bbox(x, score=None):
+    """
+    Takes a bounding box in the centre form [x,y,s,r] and returns it in the form
+      [x1,y1,x2,y2] where x1,y1 is the top left and x2,y2 is the bottom right
+    """
+    w = np.sqrt(x[2] * x[4])
+    h = x[2] / w
+    score = x[3]
+    if(score == None):
+      return np.array([x[0]-w/2., x[1]-h/2., x[0]+w/2., x[1]+h/2.]).reshape((1, 4))
+    else:
+      return np.array([x[0]-w/2., x[1]-h/2., x[0]+w/2., x[1]+h/2., score]).reshape((1, 5))
+
+
+def speed_direction(bbox1, bbox2):
+    cx1, cy1 = (bbox1[0]+bbox1[2]) / 2.0, (bbox1[1]+bbox1[3])/2.0
+    cx2, cy2 = (bbox2[0]+bbox2[2]) / 2.0, (bbox2[1]+bbox2[3])/2.0
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+def speed_direction_lt(bbox1, bbox2):
+    cx1, cy1 = bbox1[0], bbox1[1]
+    cx2, cy2 = bbox2[0], bbox2[1]
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+def speed_direction_rt(bbox1, bbox2):
+    cx1, cy1 = bbox1[0], bbox1[3]
+    cx2, cy2 = bbox2[0], bbox2[3]
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+def speed_direction_lb(bbox1, bbox2):
+    cx1, cy1 = bbox1[2], bbox1[1]
+    cx2, cy2 = bbox2[2], bbox2[1]
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+def speed_direction_rb(bbox1, bbox2):
+    cx1, cy1 = bbox1[2], bbox1[3]
+    cx2, cy2 = bbox2[2], bbox2[3]
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+class KalmanBoxTracker(object):
+    """
+    This class represents the internal state of individual tracked objects observed as bbox.
+    """
+    count = 0
+
+    def __init__(self, bbox, delta_t=3, orig=False, args=None):
+        """
+        Initialises a tracker using initial bounding box.
+
+        """
+        # define constant velocity model
+        # if not orig and not args.kalman_GPR:
+        if not orig:
+          # from .kalmanfilter import KalmanFilterNew as KalmanFilter
+          from .kalmanfilter_score_new import KalmanFilterNew_score_new as KalmanFilter_score_new
+          self.kf = KalmanFilter_score_new(dim_x=9, dim_z=5)
+          # self.kf_score = KalmanFilter_score(dim_x=2, dim_z=1)
+        else:
+          from filterpy.kalman import KalmanFilter
+          self.kf = KalmanFilter(dim_x=7, dim_z=4)
+        # u, v, s, c, r, ~u, ~v, ~s, ~c
+        self.kf.F = np.array([[1, 0, 0, 0, 0, 1, 0, 0, 0],
+                              [0, 1, 0, 0, 0, 0, 1, 0, 0],
+                              [0, 0, 1, 0, 0, 0, 0, 1, 0],
+                              [0, 0, 0, 1, 0, 0, 0, 0, 1],
+                              [0, 0, 0, 0, 1, 0, 0, 0, 0],
+                              [0, 0, 0, 0, 0, 1, 0, 0, 0],
+                              [0, 0, 0, 0, 0, 0, 1, 0, 0],
+                              [0, 0, 0, 0, 0, 0, 0, 1, 0],
+                              [0, 0, 0, 0, 0, 0, 0, 0, 1]])
+        self.kf.H = np.array([[1, 0, 0, 0, 0, 0, 0, 0, 0],
+                              [0, 1, 0, 0, 0, 0, 0, 0, 0],
+                              [0, 0, 1, 0, 0, 0, 0, 0, 0],
+                              [0, 0, 0, 1, 0, 0, 0, 0, 0],
+                              [0, 0, 0, 0, 1, 0, 0, 0, 0]])
+        # self.kf_score.F = np.array([[1, 1],
+        #                             [0, 1]])
+        # self.kf_score.H = np.array([[1, 0]])
+
+        self.kf.R[2:, 2:] *= 10.
+        self.kf.P[5:, 5:] *= 1000.  # give high uncertainty to the unobservable initial velocities
+        self.kf.P *= 10.
+        self.kf.Q[-1, -1] *= 0.01
+        self.kf.Q[-2, -2] *= 0.01
+        self.kf.Q[5:, 5:] *= 0.01
+
+        self.kf.x[:5] = convert_bbox_to_z(bbox)
+
+
+        # self.kf_score.R[0:, 0:] *= 10.
+        # self.kf_score.P[1:, 1:] *= 1000.  # give high uncertainty to the unobservable initial velocities
+        # self.kf_score.P *= 10.
+        # self.kf_score.Q[-1, -1] *= 0.01
+        # self.kf_score.Q[1:, 1:] *= 0.01
+        # self.kf_score.x[:1] = bbox[-1]
+
+
+        self.time_since_update = 0
+        self.id = KalmanBoxTracker.count
+        KalmanBoxTracker.count += 1
+        self.history = []
+        self.hits = 0
+        self.hit_streak = 0
+        self.age = 0
+        self.age_recover_for_cbiou = 0
+        """
+        NOTE: [-1,-1,-1,-1,-1] is a compromising placeholder for non-observation status, the same for the return of 
+        function k_previous_obs. It is ugly and I do not like it. But to support generate observation array in a 
+        fast and unified way, which you would see below k_observations = np.array([k_previous_obs(...]]), let's bear it for now.
+        """
+        self.last_observation = np.array([-1, -1, -1, -1, -1])  # placeholder
+        self.last_observation_save = np.array([-1, -1, -1, -1, -1])
+        self.observations = dict()
+        self.history_observations = []
+        # self.velocity = None
+        self.velocity_lt = None
+        self.velocity_rt = None
+        self.velocity_lb = None
+        self.velocity_rb = None
+        self.delta_t = delta_t
+        self.confidence_pre = None
+        self.confidence = bbox[-1]
+        self.args = args
+        self.kf.args = args
+        # self.kf_score.args = args
+
+    def update(self, bbox):
+        """
+        Updates the state vector with observed bbox.
+        """
+        # velocity = None
+        velocity_lt = None
+        velocity_rt = None
+        velocity_lb = None
+        velocity_rb = None
+        if bbox is not None:
+            if self.last_observation.sum() >= 0:  # no previous observation
+                previous_box = None
+                for i in range(self.delta_t):
+                    # dt = self.delta_t - i
+                    if self.age - i - 1 in self.observations:
+                        previous_box = self.observations[self.age - i - 1]
+                        if velocity_lt is not None:
+                            # velocity += speed_direction(previous_box, bbox)
+                            velocity_lt += speed_direction_lt(previous_box, bbox)
+                            velocity_rt += speed_direction_rt(previous_box, bbox)
+                            velocity_lb += speed_direction_lb(previous_box, bbox)
+                            velocity_rb += speed_direction_rb(previous_box, bbox)
+                        else:
+                            # velocity = speed_direction(previous_box, bbox)
+                            velocity_lt = speed_direction_lt(previous_box, bbox)
+                            velocity_rt = speed_direction_rt(previous_box, bbox)
+                            velocity_lb = speed_direction_lb(previous_box, bbox)
+                            velocity_rb = speed_direction_rb(previous_box, bbox)
+                        # break
+                if previous_box is None:
+                    previous_box = self.last_observation
+                    # self.velocity = speed_direction(previous_box, bbox)
+                    # self.velocity = norm_vel(self.velocity)
+                    self.velocity_lt = speed_direction_lt(previous_box, bbox)
+                    self.velocity_rt = speed_direction_rt(previous_box, bbox)
+                    self.velocity_lb = speed_direction_lb(previous_box, bbox)
+                    self.velocity_rb = speed_direction_rb(previous_box, bbox)
+                else:
+                    # self.velocity = velocity
+                    # self.velocity = norm_vel(self.velocity)
+                    self.velocity_lt = velocity_lt
+                    self.velocity_rt = velocity_rt
+                    self.velocity_lb = velocity_lb
+                    self.velocity_rb = velocity_rb
+            """
+              Insert new observations. This is a ugly way to maintain both self.observations
+              and self.history_observations. Bear it for the moment.
+            """
+            self.last_observation = bbox
+            self.last_observation_save = bbox
+            self.observations[self.age] = bbox
+            self.history_observations.append(bbox)
+
+            self.time_since_update = 0
+            self.history = []
+            self.hits += 1
+            self.hit_streak += 1
+            self.kf.update(convert_bbox_to_z(bbox))
+            # self.kf_score.update(bbox[-1])
+            self.confidence_pre = self.confidence
+            self.confidence = bbox[-1]
+            self.age_recover_for_cbiou = self.age
+        else:
+            self.kf.update(bbox)
+            # self.kf_score.update(bbox)
+            self.confidence_pre = None
+
+    def predict(self):
+        """
+        Advances the state vector and returns the predicted bounding box estimate.
+        """
+        if((self.kf.x[7]+self.kf.x[2]) <= 0):
+            self.kf.x[7] *= 0.0
+
+        self.kf.predict()
+        # self.kf_score.predict()
+        self.age += 1
+        if(self.time_since_update > 0):
+            self.hit_streak = 0
+        self.time_since_update += 1
+        self.history.append(convert_x_to_bbox(self.kf.x))
+        if not self.confidence_pre:
+            return self.history[-1], np.clip(self.kf.x[3], self.args.track_thresh, 1.0), np.clip(self.confidence, 0.1, self.args.track_thresh)
+        else:
+            return self.history[-1], np.clip(self.kf.x[3], self.args.track_thresh, 1.0), np.clip(self.confidence - (self.confidence_pre - self.confidence), 0.1, self.args.track_thresh)
+
+    def get_state(self):
+        """
+        Returns the current bounding box estimate.
+        """
+        return convert_x_to_bbox(self.kf.x)
+
+
+"""
+    We support multiple ways for association cost calculation, by default
+    we use IoU. GIoU may have better performance in some situations. We note 
+    that we hardly normalize the cost by all methods to (0,1) which may not be 
+    the best practice.
+"""
+ASSO_FUNCS = {  "iou": iou_batch,
+                "giou": giou_batch,
+                "ciou": ciou_batch,
+                "diou": diou_batch,
+                "ct_dist": ct_dist,
+                "Height_Modulated_IoU": hmiou
+                }
+
+
+class Hybrid_Sort(object):
+    def __init__(self, args, det_thresh, max_age=30, min_hits=3,
+        iou_threshold=0.3, delta_t=3, asso_func="iou", inertia=0.2, use_byte=False):
+        """
+        Sets key parameters for SORT
+        """
+        self.max_age = max_age
+        self.min_hits = min_hits
+        self.iou_threshold = iou_threshold
+        self.trackers = []
+        self.frame_count = 0
+        self.det_thresh = det_thresh
+        self.delta_t = delta_t
+        self.asso_func = ASSO_FUNCS[asso_func]
+        self.inertia = inertia
+        self.use_byte = use_byte
+        self.args = args
+        KalmanBoxTracker.count = 0
+
+    def update(self, output_results, img_info, img_size):
+        """
+        Params:
+          dets - a numpy array of detections in the format [[x1,y1,x2,y2,score],[x1,y1,x2,y2,score],...]
+        Requires: this method must be called once for each frame even with empty detections (use np.empty((0, 5)) for frames without detections).
+        Returns the a similar array, where the last column is the object ID.
+        NOTE: The number of objects returned may differ from the number of detections provided.
+        """
+        if output_results is None:
+            return np.empty((0, 5))
+
+        self.frame_count += 1
+        # post_process detections
+        if output_results.shape[1] == 5:
+            scores = output_results[:, 4]
+            bboxes = output_results[:, :4]
+        else:
+            output_results = output_results.cpu().numpy()
+            scores = output_results[:, 4] * output_results[:, 5]
+            bboxes = output_results[:, :4]  # x1y1x2y2
+        img_h, img_w = img_info[0], img_info[1]
+        scale = min(img_size[0] / float(img_h), img_size[1] / float(img_w))
+        bboxes /= scale
+        dets = np.concatenate((bboxes, np.expand_dims(scores, axis=-1)), axis=1)
+        inds_low = scores > 0.1
+        inds_high = scores < self.det_thresh
+        inds_second = np.logical_and(inds_low, inds_high)  # self.det_thresh > score > 0.1, for second matching
+        dets_second = dets[inds_second]  # detections for second matching
+        remain_inds = scores > self.det_thresh
+        dets = dets[remain_inds]
+
+        # get predicted locations from existing trackers.
+        trks = np.zeros((len(self.trackers), 6))
+        to_del = []
+        ret = []
+        for t, trk in enumerate(trks):
+            pos, kalman_score, simple_score = self.trackers[t].predict()
+            try:
+                trk[:] = [pos[0][0], pos[0][1], pos[0][2], pos[0][3], kalman_score, simple_score[0]]
+            except:
+                trk[:] = [pos[0][0], pos[0][1], pos[0][2], pos[0][3], kalman_score, simple_score]
+            if np.any(np.isnan(pos)):
+                to_del.append(t)
+        trks = np.ma.compress_rows(np.ma.masked_invalid(trks))
+        for t in reversed(to_del):
+            self.trackers.pop(t)
+
+        # velocities = np.array(
+        #     [trk.velocity if trk.velocity is not None else np.array((0, 0)) for trk in self.trackers])
+        velocities_lt = np.array(
+            [trk.velocity_lt if trk.velocity_lt is not None else np.array((0, 0)) for trk in self.trackers])
+        velocities_rt = np.array(
+            [trk.velocity_rt if trk.velocity_rt is not None else np.array((0, 0)) for trk in self.trackers])
+        velocities_lb = np.array(
+            [trk.velocity_lb if trk.velocity_lb is not None else np.array((0, 0)) for trk in self.trackers])
+        velocities_rb = np.array(
+            [trk.velocity_rb if trk.velocity_rb is not None else np.array((0, 0)) for trk in self.trackers])
+        last_boxes = np.array([trk.last_observation for trk in self.trackers])
+        k_observations = np.array(
+            [k_previous_obs(trk.observations, trk.age, self.delta_t) for trk in self.trackers])
+
+        """
+            First round of association
+        """
+        if self.args.TCM_first_step:
+            matched, unmatched_dets, unmatched_trks = associate_4_points_with_score(
+                dets, trks, self.iou_threshold, velocities_lt, velocities_rt, velocities_lb, velocities_rb,
+                k_observations, self.inertia, self.asso_func, self.args)
+        else:
+            matched, unmatched_dets, unmatched_trks = associate_4_points(
+                dets, trks, self.iou_threshold, velocities_lt, velocities_rt, velocities_lb, velocities_rb, k_observations, self.inertia, self.asso_func, self.args)
+
+        for m in matched:
+            self.trackers[m[1]].update(dets[m[0], :])
+
+        """
+            Second round of associaton by OCR
+        """
+        # BYTE association
+        if self.use_byte and len(dets_second) > 0 and unmatched_trks.shape[0] > 0:
+            u_trks = trks[unmatched_trks]
+            iou_left = self.asso_func(dets_second, u_trks)
+            iou_left = np.array(iou_left)
+            if iou_left.max() > self.iou_threshold:
+                """
+                    NOTE: by using a lower threshold, e.g., self.iou_threshold - 0.1, you may
+                    get a higher performance especially on MOT17/MOT20 datasets. But we keep it
+                    uniform here for simplicity
+                """
+                if self.args.TCM_byte_step:
+                    iou_left -= np.array(cal_score_dif_batch_two_score(dets_second, u_trks) * self.args.TCM_byte_step_weight)
+                matched_indices = linear_assignment(-iou_left)
+                to_remove_trk_indices = []
+                for m in matched_indices:
+                    det_ind, trk_ind = m[0], unmatched_trks[m[1]]
+                    if iou_left[m[0], m[1]] < self.iou_threshold:
+                        continue
+                    self.trackers[trk_ind].update(dets_second[det_ind, :])
+                    to_remove_trk_indices.append(trk_ind)
+                unmatched_trks = np.setdiff1d(unmatched_trks, np.array(to_remove_trk_indices))
+
+        if unmatched_dets.shape[0] > 0 and unmatched_trks.shape[0] > 0:
+            left_dets = dets[unmatched_dets]
+            left_trks = last_boxes[unmatched_trks]
+            iou_left = self.asso_func(left_dets, left_trks)
+            iou_left = np.array(iou_left)
+
+            if iou_left.max() > self.iou_threshold:
+                """
+                    NOTE: by using a lower threshold, e.g., self.iou_threshold - 0.1, you may
+                    get a higher performance especially on MOT17/MOT20 datasets. But we keep it
+                    uniform here for simplicity
+                """
+                rematched_indices = linear_assignment(-iou_left)
+                to_remove_det_indices = []
+                to_remove_trk_indices = []
+                for m in rematched_indices:
+                    det_ind, trk_ind = unmatched_dets[m[0]], unmatched_trks[m[1]]
+                    if iou_left[m[0], m[1]] < self.iou_threshold:
+                        continue
+                    self.trackers[trk_ind].update(dets[det_ind, :])
+                    to_remove_det_indices.append(det_ind)
+                    to_remove_trk_indices.append(trk_ind)
+                unmatched_dets = np.setdiff1d(unmatched_dets, np.array(to_remove_det_indices))
+                unmatched_trks = np.setdiff1d(unmatched_trks, np.array(to_remove_trk_indices))
+
+        for m in unmatched_trks:
+            self.trackers[m].update(None)
+
+        # create and initialise new trackers for unmatched detections
+        for i in unmatched_dets:
+            trk = KalmanBoxTracker(dets[i, :], delta_t=self.delta_t, args=self.args)
+            self.trackers.append(trk)
+        i = len(self.trackers)
+        for trk in reversed(self.trackers):
+            if trk.last_observation.sum() < 0:
+                d = trk.get_state()[0][:4]
+            else:
+                """
+                    this is optional to use the recent observation or the kalman filter prediction,
+                    we didn't notice significant difference here
+                """
+                d = trk.last_observation[:4]
+            if (trk.time_since_update < 1) and (trk.hit_streak >= self.min_hits or self.frame_count <= self.min_hits):
+                # +1 as MOT benchmark requires positive
+                ret.append(np.concatenate((d, [trk.id+1])).reshape(1, -1))
+            i -= 1
+            # remove dead tracklet
+            if(trk.time_since_update > self.max_age):
+                self.trackers.pop(i)
+        if(len(ret) > 0):
+            return np.concatenate(ret)
+        return np.empty((0, 5))
+
+    def update_public(self, dets, cates, scores):
+        self.frame_count += 1
+
+        det_scores = np.ones((dets.shape[0], 1))
+        dets = np.concatenate((dets, det_scores), axis=1)
+
+        remain_inds = scores > self.det_thresh
+        
+        cates = cates[remain_inds]
+        dets = dets[remain_inds]
+
+        trks = np.zeros((len(self.trackers), 5))
+        to_del = []
+        ret = []
+        for t, trk in enumerate(trks):
+            pos = self.trackers[t].predict()[0]
+            cat = self.trackers[t].cate
+            trk[:] = [pos[0], pos[1], pos[2], pos[3], cat]
+            if np.any(np.isnan(pos)):
+                to_del.append(t)
+        trks = np.ma.compress_rows(np.ma.masked_invalid(trks))
+        for t in reversed(to_del):
+            self.trackers.pop(t)
+
+        velocities = np.array([trk.velocity if trk.velocity is not None else np.array((0,0)) for trk in self.trackers])
+        last_boxes = np.array([trk.last_observation for trk in self.trackers])
+        k_observations = np.array([k_previous_obs(trk.observations, trk.age, self.delta_t) for trk in self.trackers])
+
+        matched, unmatched_dets, unmatched_trks = associate_kitti\
+              (dets, trks, cates, self.iou_threshold, velocities, k_observations, self.inertia)
+          
+        for m in matched:
+            self.trackers[m[1]].update(dets[m[0], :])
+          
+        if unmatched_dets.shape[0] > 0 and unmatched_trks.shape[0] > 0:
+            """
+                The re-association stage by OCR.
+                NOTE: at this stage, adding other strategy might be able to continue improve
+                the performance, such as BYTE association by ByteTrack. 
+            """
+            left_dets = dets[unmatched_dets]
+            left_trks = last_boxes[unmatched_trks]
+            left_dets_c = left_dets.copy()
+            left_trks_c = left_trks.copy()
+
+            iou_left = self.asso_func(left_dets_c, left_trks_c)
+            iou_left = np.array(iou_left)
+            det_cates_left = cates[unmatched_dets]
+            trk_cates_left = trks[unmatched_trks][:,4]
+            num_dets = unmatched_dets.shape[0]
+            num_trks = unmatched_trks.shape[0]
+            cate_matrix = np.zeros((num_dets, num_trks))
+            for i in range(num_dets):
+                for j in range(num_trks):
+                    if det_cates_left[i] != trk_cates_left[j]:
+                            """
+                                For some datasets, such as KITTI, there are different categories,
+                                we have to avoid associate them together.
+                            """
+                            cate_matrix[i][j] = -1e6
+            iou_left = iou_left + cate_matrix
+            if iou_left.max() > self.iou_threshold - 0.1:
+                rematched_indices = linear_assignment(-iou_left)
+                to_remove_det_indices = []
+                to_remove_trk_indices = []
+                for m in rematched_indices:
+                    det_ind, trk_ind = unmatched_dets[m[0]], unmatched_trks[m[1]]
+                    if iou_left[m[0], m[1]] < self.iou_threshold - 0.1:
+                          continue
+                    self.trackers[trk_ind].update(dets[det_ind, :])
+                    to_remove_det_indices.append(det_ind)
+                    to_remove_trk_indices.append(trk_ind) 
+                unmatched_dets = np.setdiff1d(unmatched_dets, np.array(to_remove_det_indices))
+                unmatched_trks = np.setdiff1d(unmatched_trks, np.array(to_remove_trk_indices))
+
+        for i in unmatched_dets:
+            trk = KalmanBoxTracker(dets[i,:])
+            trk.cate = cates[i]
+            self.trackers.append(trk)
+        i = len(self.trackers)
+
+        for trk in reversed(self.trackers):
+            if trk.last_observation.sum() > 0:
+                d = trk.last_observation[:4]
+            else:
+                d = trk.get_state()[0]
+            if (trk.time_since_update < 1):
+                if (self.frame_count <= self.min_hits) or (trk.hit_streak >= self.min_hits):
+                    # id+1 as MOT benchmark requires positive
+                    ret.append(np.concatenate((d, [trk.id+1], [trk.cate], [0])).reshape(1,-1)) 
+                if trk.hit_streak == self.min_hits:
+                    # Head Padding (HP): recover the lost steps during initializing the track
+                    for prev_i in range(self.min_hits - 1):
+                        prev_observation = trk.history_observations[-(prev_i+2)]
+                        ret.append((np.concatenate((prev_observation[:4], [trk.id+1], [trk.cate], 
+                            [-(prev_i+1)]))).reshape(1,-1))
+            i -= 1 
+            if (trk.time_since_update > self.max_age):
+                  self.trackers.pop(i)
+        
+        if(len(ret)>0):
+            return np.concatenate(ret)
+        return np.empty((0, 7))
+
+
diff --git a/trackers/hybrid_sort_tracker/hybrid_sort_reid.py b/trackers/hybrid_sort_tracker/hybrid_sort_reid.py
new file mode 100644
index 0000000000000000000000000000000000000000..854ce40f0bc727666be75f779a1be323553b74d8
--- /dev/null
+++ b/trackers/hybrid_sort_tracker/hybrid_sort_reid.py
@@ -0,0 +1,630 @@
+"""
+    This script is adopted from the SORT script by Alex Bewley alex@bewley.ai
+"""
+from __future__ import print_function
+
+import numpy as np
+import copy
+from .association import *
+from collections import deque       # [hgx0418] deque for reid feature
+np.random.seed(0)
+
+def k_previous_obs(observations, cur_age, k):
+    if len(observations) == 0:
+        return [-1, -1, -1, -1, -1]
+    for i in range(k):
+        dt = k - i
+        if cur_age - dt in observations:
+            return observations[cur_age-dt]
+    max_age = max(observations.keys())
+    return observations[max_age]
+
+
+def convert_bbox_to_z(bbox):
+    """
+    Takes a bounding box in the form [x1,y1,x2,y2] and returns z in the form
+      [x,y,s,r] where x,y is the centre of the box and s is the scale/area and r is
+      the aspect ratio
+    """
+    w = bbox[2] - bbox[0]
+    h = bbox[3] - bbox[1]
+    x = bbox[0] + w/2.
+    y = bbox[1] + h/2.
+    s = w * h  # scale is just area
+    r = w / float(h+1e-6)
+    score = bbox[4]
+    if score:
+        return np.array([x, y, s, score, r]).reshape((5, 1))
+    else:
+        return np.array([x, y, s, r]).reshape((4, 1))
+
+
+def convert_x_to_bbox(x, score=None):
+    """
+    Takes a bounding box in the centre form [x,y,s,r] and returns it in the form
+      [x1,y1,x2,y2] where x1,y1 is the top left and x2,y2 is the bottom right
+    """
+    w = np.sqrt(x[2] * x[4])
+    h = x[2] / w
+    score = x[3]
+    if(score == None):
+      return np.array([x[0]-w/2., x[1]-h/2., x[0]+w/2., x[1]+h/2.]).reshape((1, 4))
+    else:
+      return np.array([x[0]-w/2., x[1]-h/2., x[0]+w/2., x[1]+h/2., score]).reshape((1, 5))
+
+
+def speed_direction(bbox1, bbox2):
+    cx1, cy1 = (bbox1[0]+bbox1[2]) / 2.0, (bbox1[1]+bbox1[3])/2.0
+    cx2, cy2 = (bbox2[0]+bbox2[2]) / 2.0, (bbox2[1]+bbox2[3])/2.0
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+def speed_direction_lt(bbox1, bbox2):
+    cx1, cy1 = bbox1[0], bbox1[1]
+    cx2, cy2 = bbox2[0], bbox2[1]
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+def speed_direction_rt(bbox1, bbox2):
+    cx1, cy1 = bbox1[0], bbox1[3]
+    cx2, cy2 = bbox2[0], bbox2[3]
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+def speed_direction_lb(bbox1, bbox2):
+    cx1, cy1 = bbox1[2], bbox1[1]
+    cx2, cy2 = bbox2[2], bbox2[1]
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+def speed_direction_rb(bbox1, bbox2):
+    cx1, cy1 = bbox1[2], bbox1[3]
+    cx2, cy2 = bbox2[2], bbox2[3]
+    speed = np.array([cy2-cy1, cx2-cx1])
+    norm = np.sqrt((cy2-cy1)**2 + (cx2-cx1)**2) + 1e-6
+    return speed / norm
+
+class KalmanBoxTracker(object):
+    """
+    This class represents the internal state of individual tracked objects observed as bbox.
+    """
+    count = 0
+
+    def __init__(self, bbox, temp_feat, delta_t=3, orig=False, buffer_size=30, args=None):     # 'temp_feat' and 'buffer_size' for reid feature
+        """
+        Initialises a tracker using initial bounding box.
+
+        """
+        # define constant velocity model
+        # if not orig and not args.kalman_GPR:
+        if not orig:
+          from .kalmanfilter_score_new import KalmanFilterNew_score_new as KalmanFilter_score_new
+          self.kf = KalmanFilter_score_new(dim_x=9, dim_z=5)
+        else:
+          from filterpy.kalman import KalmanFilter
+          self.kf = KalmanFilter(dim_x=7, dim_z=4)
+        # u, v, s, c, r, ~u, ~v, ~s, ~c
+        self.kf.F = np.array([[1, 0, 0, 0, 0, 1, 0, 0, 0],
+                              [0, 1, 0, 0, 0, 0, 1, 0, 0],
+                              [0, 0, 1, 0, 0, 0, 0, 1, 0],
+                              [0, 0, 0, 1, 0, 0, 0, 0, 1],
+                              [0, 0, 0, 0, 1, 0, 0, 0, 0],
+                              [0, 0, 0, 0, 0, 1, 0, 0, 0],
+                              [0, 0, 0, 0, 0, 0, 1, 0, 0],
+                              [0, 0, 0, 0, 0, 0, 0, 1, 0],
+                              [0, 0, 0, 0, 0, 0, 0, 0, 1]])
+        self.kf.H = np.array([[1, 0, 0, 0, 0, 0, 0, 0, 0],
+                              [0, 1, 0, 0, 0, 0, 0, 0, 0],
+                              [0, 0, 1, 0, 0, 0, 0, 0, 0],
+                              [0, 0, 0, 1, 0, 0, 0, 0, 0],
+                              [0, 0, 0, 0, 1, 0, 0, 0, 0]])
+
+        self.kf.R[2:, 2:] *= 10.
+        self.kf.P[5:, 5:] *= 1000.  # give high uncertainty to the unobservable initial velocities
+        self.kf.P *= 10.
+        self.kf.Q[-1, -1] *= 0.01
+        self.kf.Q[-2, -2] *= 0.01
+        self.kf.Q[5:, 5:] *= 0.01
+
+        self.kf.x[:5] = convert_bbox_to_z(bbox)
+
+        self.time_since_update = 0
+        self.id = KalmanBoxTracker.count
+        KalmanBoxTracker.count += 1
+        self.history = []
+        self.hits = 0
+        self.hit_streak = 0
+        self.age = 0
+        """
+        NOTE: [-1,-1,-1,-1,-1] is a compromising placeholder for non-observation status, the same for the return of 
+        function k_previous_obs. It is ugly and I do not like it. But to support generate observation array in a 
+        fast and unified way, which you would see below k_observations = np.array([k_previous_obs(...]]), let's bear it for now.
+        """
+        self.last_observation = np.array([-1, -1, -1, -1, -1])  # placeholder
+        self.last_observation_save = np.array([-1, -1, -1, -1, -1])
+        self.observations = dict()
+        self.history_observations = []
+        self.velocity_lt = None
+        self.velocity_rt = None
+        self.velocity_lb = None
+        self.velocity_rb = None
+        self.delta_t = delta_t
+        self.confidence_pre = None
+        self.confidence = bbox[-1]
+        self.args = args
+        self.kf.args = args
+
+        # add the following values and functions
+        self.smooth_feat = None
+        buffer_size = args.longterm_bank_length
+        self.features = deque([], maxlen=buffer_size)
+        self.update_features(temp_feat)
+
+        # momentum of embedding update
+        self.alpha = self.args.alpha
+
+    # ReID. for update embeddings during tracking
+    def update_features(self, feat, score=-1):
+        feat /= np.linalg.norm(feat)
+        self.curr_feat = feat
+        if self.smooth_feat is None:
+            self.smooth_feat = feat
+        else:
+            if self.args.adapfs:
+                assert score > 0
+                pre_w = self.alpha * (self.confidence / (self.confidence + score))
+                cur_w = (1 - self.alpha) * (score / (self.confidence + score))
+                sum_w = pre_w + cur_w
+                pre_w = pre_w / sum_w
+                cur_w = cur_w / sum_w
+                self.smooth_feat = pre_w * self.smooth_feat + cur_w * feat
+            else:
+                self.smooth_feat = self.alpha * self.smooth_feat + (1 - self.alpha) * feat
+        self.features.append(feat)
+        self.smooth_feat /= np.linalg.norm(self.smooth_feat)
+
+    def camera_update(self, warp_matrix):
+        """
+        update 'self.mean' of current tracklet with ecc results.
+        Parameters
+        ----------
+        warp_matrix: warp matrix computed by ECC.
+        """
+        x1, y1, x2, y2, s = convert_x_to_bbox(self.kf.x)[0]
+        x1_, y1_, _ = warp_matrix @ np.array([x1, y1, 1]).T
+        x2_, y2_, _ = warp_matrix @ np.array([x2, y2, 1]).T
+        # w, h = x2_ - x1_, y2_ - y1_
+        # cx, cy = x1_ + w / 2, y1_ + h / 2
+        self.kf.x[:5] = convert_bbox_to_z([x1_, y1_, x2_, y2_, s])
+
+    def update(self, bbox, id_feature, update_feature=True):
+        """
+        Updates the state vector with observed bbox.
+        """
+        velocity_lt = None
+        velocity_rt = None
+        velocity_lb = None
+        velocity_rb = None
+        if bbox is not None:
+            if self.last_observation.sum() >= 0:  # no previous observation
+                previous_box = None
+                for i in range(self.delta_t):
+                    # dt = self.delta_t - i
+                    if self.age - i - 1 in self.observations:
+                        previous_box = self.observations[self.age - i - 1]
+                        if velocity_lt is not None:
+                            velocity_lt += speed_direction_lt(previous_box, bbox)
+                            velocity_rt += speed_direction_rt(previous_box, bbox)
+                            velocity_lb += speed_direction_lb(previous_box, bbox)
+                            velocity_rb += speed_direction_rb(previous_box, bbox)
+                        else:
+                            velocity_lt = speed_direction_lt(previous_box, bbox)
+                            velocity_rt = speed_direction_rt(previous_box, bbox)
+                            velocity_lb = speed_direction_lb(previous_box, bbox)
+                            velocity_rb = speed_direction_rb(previous_box, bbox)
+                        # break
+                if previous_box is None:
+                    previous_box = self.last_observation
+                    self.velocity_lt = speed_direction_lt(previous_box, bbox)
+                    self.velocity_rt = speed_direction_rt(previous_box, bbox)
+                    self.velocity_lb = speed_direction_lb(previous_box, bbox)
+                    self.velocity_rb = speed_direction_rb(previous_box, bbox)
+                else:
+                    self.velocity_lt = velocity_lt
+                    self.velocity_rt = velocity_rt
+                    self.velocity_lb = velocity_lb
+                    self.velocity_rb = velocity_rb
+            """
+              Insert new observations. This is a ugly way to maintain both self.observations
+              and self.history_observations. Bear it for the moment.
+            """
+            self.last_observation = bbox
+            self.last_observation_save = bbox
+            self.observations[self.age] = bbox
+            self.history_observations.append(bbox)
+
+            self.time_since_update = 0
+            self.history = []
+            self.hits += 1
+            self.hit_streak += 1
+            self.kf.update(convert_bbox_to_z(bbox))
+            # add interface for update feature or not
+            if update_feature:
+                if self.args.adapfs:
+                    self.update_features(id_feature, score=bbox[-1])
+                else:
+                    self.update_features(id_feature)
+            self.confidence_pre = self.confidence
+            self.confidence = bbox[-1]
+        else:
+            self.kf.update(bbox)
+            self.confidence_pre = None
+
+    def predict(self):
+        """
+        Advances the state vector and returns the predicted bounding box estimate.
+        """
+        if((self.kf.x[7]+self.kf.x[2]) <= 0):
+            self.kf.x[7] *= 0.0
+
+        self.kf.predict()
+        self.age += 1
+        if(self.time_since_update > 0):
+            self.hit_streak = 0
+        self.time_since_update += 1
+        self.history.append(convert_x_to_bbox(self.kf.x))
+        if not self.confidence_pre:
+            return self.history[-1], np.clip(self.kf.x[3], self.args.track_thresh, 1.0), np.clip(self.confidence, 0.1, self.args.track_thresh)
+        else:
+            return self.history[-1], np.clip(self.kf.x[3], self.args.track_thresh, 1.0), np.clip(self.confidence - (self.confidence_pre - self.confidence), 0.1, self.args.track_thresh)
+
+    def get_state(self):
+        """
+        Returns the current bounding box estimate.
+        """
+        return convert_x_to_bbox(self.kf.x)
+
+
+"""
+    We support multiple ways for association cost calculation, by default
+    we use IoU. GIoU may have better performance in some situations. We note 
+    that we hardly normalize the cost by all methods to (0,1) which may not be 
+    the best practice.
+"""
+ASSO_FUNCS = {  "iou": iou_batch,
+                "giou": giou_batch,
+                "ciou": ciou_batch,
+                "diou": diou_batch,
+                "ct_dist": ct_dist,
+                "Height_Modulated_IoU": hmiou
+                }
+
+
+class Hybrid_Sort_ReID(object):
+    def __init__(self, args, det_thresh, max_age=30, min_hits=3,
+        iou_threshold=0.3, delta_t=3, asso_func="iou", inertia=0.2):
+        """
+        Sets key parameters for SORT
+        """
+        self.max_age = max_age
+        self.min_hits = min_hits
+        self.iou_threshold = iou_threshold
+        self.trackers = []
+        self.frame_count = 0
+        self.det_thresh = det_thresh
+        self.delta_t = delta_t
+        self.asso_func = ASSO_FUNCS[asso_func]
+        self.inertia = inertia
+        self.use_byte = args.use_byte
+        self.args = args
+        KalmanBoxTracker.count = 0
+
+    # ECC for CMC
+    def camera_update(self, trackers, warp_matrix):
+        for tracker in trackers:
+            tracker.camera_update(warp_matrix)
+
+    def update(self, output_results, img_info, img_size, id_feature=None, warp_matrix=None):
+        """
+        Params:
+          dets - a numpy array of detections in the format [[x1,y1,x2,y2,score],[x1,y1,x2,y2,score],...]
+        Requires: this method must be called once for each frame even with empty detections (use np.empty((0, 5)) for frames without detections).
+        Returns the a similar array, where the last column is the object ID.
+        NOTE: The number of objects returned may differ from the number of detections provided.
+        """
+        if output_results is None:
+            return np.empty((0, 5))
+
+        if self.args.ECC:
+            # camera update for all stracks
+            if warp_matrix is not None:
+                self.camera_update(self.trackers, warp_matrix)
+
+        self.frame_count += 1
+        # post_process detections
+        if output_results.shape[1] == 5:
+            scores = output_results[:, 4]
+            bboxes = output_results[:, :4]
+        else:
+            output_results = output_results.cpu().numpy()
+            scores = output_results[:, 4] * output_results[:, 5]
+            bboxes = output_results[:, :4]  # x1y1x2y2
+        img_h, img_w = img_info[0], img_info[1]
+        scale = min(img_size[0] / float(img_h), img_size[1] / float(img_w))
+        bboxes /= scale
+        dets = np.concatenate((bboxes, np.expand_dims(scores, axis=-1)), axis=1)
+        inds_low = scores > self.args.low_thresh
+        inds_high = scores < self.det_thresh
+        inds_second = np.logical_and(inds_low, inds_high)  # self.det_thresh > score > 0.1, for second matching
+        dets_second = dets[inds_second]  # detections for second matching
+        remain_inds = scores > self.det_thresh
+        dets = dets[remain_inds]
+        id_feature_keep = id_feature[remain_inds]  # ID feature of 1st stage matching
+        id_feature_second = id_feature[inds_second]  # ID feature of 2nd stage matching
+
+        trks = np.zeros((len(self.trackers), 6))
+        to_del = []
+        ret = []
+        for t, trk in enumerate(trks):
+            pos, kalman_score, simple_score = self.trackers[t].predict()
+            try:
+                trk[:] = [pos[0][0], pos[0][1], pos[0][2], pos[0][3], kalman_score, simple_score[0]]
+            except:
+                trk[:] = [pos[0][0], pos[0][1], pos[0][2], pos[0][3], kalman_score, simple_score]
+            if np.any(np.isnan(pos)):
+                to_del.append(t)
+        trks = np.ma.compress_rows(np.ma.masked_invalid(trks))
+        for t in reversed(to_del):
+            self.trackers.pop(t)
+
+        velocities_lt = np.array(
+            [trk.velocity_lt if trk.velocity_lt is not None else np.array((0, 0)) for trk in self.trackers])
+        velocities_rt = np.array(
+            [trk.velocity_rt if trk.velocity_rt is not None else np.array((0, 0)) for trk in self.trackers])
+        velocities_lb = np.array(
+            [trk.velocity_lb if trk.velocity_lb is not None else np.array((0, 0)) for trk in self.trackers])
+        velocities_rb = np.array(
+            [trk.velocity_rb if trk.velocity_rb is not None else np.array((0, 0)) for trk in self.trackers])
+        last_boxes = np.array([trk.last_observation for trk in self.trackers])
+        k_observations = np.array(
+            [k_previous_obs(trk.observations, trk.age, self.delta_t) for trk in self.trackers])
+
+        """
+            First round of association
+        """
+        if self.args.EG_weight_high_score > 0 and self.args.TCM_first_step:
+            track_features = np.asarray([track.smooth_feat for track in self.trackers],
+                                        dtype=np.float)
+            emb_dists = embedding_distance(track_features, id_feature_keep).T
+            if self.args.with_longterm_reid or self.args.with_longterm_reid_correction:
+                long_track_features = np.asarray([np.vstack(list(track.features)).mean(0) for track in self.trackers],
+                                                 dtype=np.float)
+                assert track_features.shape == long_track_features.shape
+                long_emb_dists = embedding_distance(long_track_features, id_feature_keep).T
+                assert emb_dists.shape == long_emb_dists.shape
+                matched, unmatched_dets, unmatched_trks = associate_4_points_with_score_with_reid(
+                    dets, trks, self.iou_threshold, velocities_lt, velocities_rt, velocities_lb, velocities_rb,
+                    k_observations, self.inertia, self.asso_func, self.args,emb_cost=emb_dists,
+                    weights=(1.0, self.args.EG_weight_high_score), thresh=self.args.high_score_matching_thresh,
+                    long_emb_dists=long_emb_dists, with_longterm_reid=self.args.with_longterm_reid,
+                    longterm_reid_weight=self.args.longterm_reid_weight,
+                    with_longterm_reid_correction=self.args.with_longterm_reid_correction,
+                    longterm_reid_correction_thresh=self.args.longterm_reid_correction_thresh,
+                    dataset=self.args.dataset)
+            else:
+                matched, unmatched_dets, unmatched_trks = associate_4_points_with_score_with_reid(
+                    dets, trks, self.iou_threshold, velocities_lt, velocities_rt, velocities_lb, velocities_rb,
+                    k_observations, self.inertia, self.asso_func, self.args,emb_cost=emb_dists,
+                    weights=(1.0, self.args.EG_weight_high_score), thresh=self.args.high_score_matching_thresh)
+        elif self.args.TCM_first_step:
+            matched, unmatched_dets, unmatched_trks = associate_4_points_with_score(
+                dets, trks, self.iou_threshold, velocities_lt, velocities_rt, velocities_lb, velocities_rb,
+                k_observations, self.inertia, self.asso_func, self.args)
+
+        # update with id feature
+        for m in matched:
+            self.trackers[m[1]].update(dets[m[0], :], id_feature_keep[m[0], :])
+
+        """
+            Second round of associaton by OCR
+        """
+        # BYTE association
+        if self.use_byte and len(dets_second) > 0 and unmatched_trks.shape[0] > 0:
+            u_trks = trks[unmatched_trks]
+            u_tracklets = [self.trackers[index] for index in unmatched_trks]
+            iou_left = self.asso_func(dets_second, u_trks)
+            iou_left = np.array(iou_left)
+            if iou_left.max() > self.iou_threshold:
+                """
+                    NOTE: by using a lower threshold, e.g., self.iou_threshold - 0.1, you may
+                    get a higher performance especially on MOT17/MOT20 datasets. But we keep it
+                    uniform here for simplicity
+                """
+                if self.args.TCM_byte_step:
+                    iou_left_ori = copy.deepcopy(iou_left)
+                    iou_left -= np.array(cal_score_dif_batch_two_score(dets_second, u_trks) * self.args.TCM_byte_step_weight)
+                    iou_left_thre = iou_left
+                if self.args.EG_weight_low_score > 0:
+                    u_track_features = np.asarray([track.smooth_feat for track in u_tracklets], dtype=np.float)
+                    emb_dists_low_score = embedding_distance(u_track_features, id_feature_second).T
+                    matched_indices = linear_assignment(-iou_left + self.args.EG_weight_low_score * emb_dists_low_score,
+                                                        )
+                else:
+                    matched_indices = linear_assignment(-iou_left)
+                to_remove_trk_indices = []
+                for m in matched_indices:
+                    det_ind, trk_ind = m[0], unmatched_trks[m[1]]
+                    if self.args.with_longterm_reid_correction and self.args.EG_weight_low_score > 0:
+                        if iou_left_thre[m[0], m[1]] < self.iou_threshold or emb_dists_low_score[m[0], m[1]] > self.args.longterm_reid_correction_thresh_low:
+                            print("correction 2nd:", emb_dists_low_score[m[0], m[1]])
+                            continue
+                    else:
+                        if iou_left_thre[m[0], m[1]] < self.iou_threshold:
+                            continue
+                    self.trackers[trk_ind].update(dets_second[det_ind, :], id_feature_second[det_ind, :], update_feature=False)     # [hgx0523] do not update with id feature
+                    to_remove_trk_indices.append(trk_ind)
+                unmatched_trks = np.setdiff1d(unmatched_trks, np.array(to_remove_trk_indices))
+
+        if unmatched_dets.shape[0] > 0 and unmatched_trks.shape[0] > 0:
+            left_dets = dets[unmatched_dets]
+            # left_id_feature = id_feature_keep[unmatched_dets]       # update id feature, if needed
+            left_trks = last_boxes[unmatched_trks]
+            iou_left = self.asso_func(left_dets, left_trks)
+            iou_left = np.array(iou_left)
+
+            if iou_left.max() > self.iou_threshold:
+                """
+                    NOTE: by using a lower threshold, e.g., self.iou_threshold - 0.1, you may
+                    get a higher performance especially on MOT17/MOT20 datasets. But we keep it
+                    uniform here for simplicity
+                """
+                rematched_indices = linear_assignment(-iou_left)
+                to_remove_det_indices = []
+                to_remove_trk_indices = []
+                for m in rematched_indices:
+                    det_ind, trk_ind = unmatched_dets[m[0]], unmatched_trks[m[1]]
+                    if iou_left[m[0], m[1]] < self.iou_threshold:
+                        continue
+                    self.trackers[trk_ind].update(dets[det_ind, :], id_feature_keep[det_ind, :], update_feature=False)
+                    to_remove_det_indices.append(det_ind)
+                    to_remove_trk_indices.append(trk_ind)
+                unmatched_dets = np.setdiff1d(unmatched_dets, np.array(to_remove_det_indices))
+                unmatched_trks = np.setdiff1d(unmatched_trks, np.array(to_remove_trk_indices))
+
+        for m in unmatched_trks:
+            self.trackers[m].update(None, None)
+
+        # create and initialise new trackers for unmatched detections
+        for i in unmatched_dets:
+            trk = KalmanBoxTracker(dets[i, :], id_feature_keep[i, :], delta_t=self.delta_t, args=self.args)
+            self.trackers.append(trk)
+        i = len(self.trackers)
+        for trk in reversed(self.trackers):
+            if trk.last_observation.sum() < 0:
+                d = trk.get_state()[0][:4]
+            else:
+                """
+                    this is optional to use the recent observation or the kalman filter prediction,
+                    we didn't notice significant difference here
+                """
+                d = trk.last_observation[:4]
+            if (trk.time_since_update < 1) and (trk.hit_streak >= self.min_hits or self.frame_count <= self.min_hits):
+                # +1 as MOT benchmark requires positive
+                ret.append(np.concatenate((d, [trk.id+1])).reshape(1, -1))
+            i -= 1
+            # remove dead tracklet
+            if(trk.time_since_update > self.max_age):
+                self.trackers.pop(i)
+        if(len(ret) > 0):
+            return np.concatenate(ret)
+        return np.empty((0, 5))
+
+    def update_public(self, dets, cates, scores):
+        self.frame_count += 1
+
+        det_scores = np.ones((dets.shape[0], 1))
+        dets = np.concatenate((dets, det_scores), axis=1)
+
+        remain_inds = scores > self.det_thresh
+        
+        cates = cates[remain_inds]
+        dets = dets[remain_inds]
+
+        trks = np.zeros((len(self.trackers), 5))
+        to_del = []
+        ret = []
+        for t, trk in enumerate(trks):
+            pos = self.trackers[t].predict()[0]
+            cat = self.trackers[t].cate
+            trk[:] = [pos[0], pos[1], pos[2], pos[3], cat]
+            if np.any(np.isnan(pos)):
+                to_del.append(t)
+        trks = np.ma.compress_rows(np.ma.masked_invalid(trks))
+        for t in reversed(to_del):
+            self.trackers.pop(t)
+
+        velocities = np.array([trk.velocity if trk.velocity is not None else np.array((0,0)) for trk in self.trackers])
+        last_boxes = np.array([trk.last_observation for trk in self.trackers])
+        k_observations = np.array([k_previous_obs(trk.observations, trk.age, self.delta_t) for trk in self.trackers])
+
+        matched, unmatched_dets, unmatched_trks = associate_kitti\
+              (dets, trks, cates, self.iou_threshold, velocities, k_observations, self.inertia)
+          
+        for m in matched:
+            self.trackers[m[1]].update(dets[m[0], :])
+          
+        if unmatched_dets.shape[0] > 0 and unmatched_trks.shape[0] > 0:
+            """
+                The re-association stage by OCR.
+                NOTE: at this stage, adding other strategy might be able to continue improve
+                the performance, such as BYTE association by ByteTrack. 
+            """
+            left_dets = dets[unmatched_dets]
+            left_trks = last_boxes[unmatched_trks]
+            left_dets_c = left_dets.copy()
+            left_trks_c = left_trks.copy()
+
+            iou_left = self.asso_func(left_dets_c, left_trks_c)
+            iou_left = np.array(iou_left)
+            det_cates_left = cates[unmatched_dets]
+            trk_cates_left = trks[unmatched_trks][:,4]
+            num_dets = unmatched_dets.shape[0]
+            num_trks = unmatched_trks.shape[0]
+            cate_matrix = np.zeros((num_dets, num_trks))
+            for i in range(num_dets):
+                for j in range(num_trks):
+                    if det_cates_left[i] != trk_cates_left[j]:
+                            """
+                                For some datasets, such as KITTI, there are different categories,
+                                we have to avoid associate them together.
+                            """
+                            cate_matrix[i][j] = -1e6
+            iou_left = iou_left + cate_matrix
+            if iou_left.max() > self.iou_threshold - 0.1:
+                rematched_indices = linear_assignment(-iou_left)
+                to_remove_det_indices = []
+                to_remove_trk_indices = []
+                for m in rematched_indices:
+                    det_ind, trk_ind = unmatched_dets[m[0]], unmatched_trks[m[1]]
+                    if iou_left[m[0], m[1]] < self.iou_threshold - 0.1:
+                          continue
+                    self.trackers[trk_ind].update(dets[det_ind, :])
+                    to_remove_det_indices.append(det_ind)
+                    to_remove_trk_indices.append(trk_ind) 
+                unmatched_dets = np.setdiff1d(unmatched_dets, np.array(to_remove_det_indices))
+                unmatched_trks = np.setdiff1d(unmatched_trks, np.array(to_remove_trk_indices))
+
+        for i in unmatched_dets:
+            trk = KalmanBoxTracker(dets[i,:])
+            trk.cate = cates[i]
+            self.trackers.append(trk)
+        i = len(self.trackers)
+
+        for trk in reversed(self.trackers):
+            if trk.last_observation.sum() > 0:
+                d = trk.last_observation[:4]
+            else:
+                d = trk.get_state()[0]
+            if (trk.time_since_update < 1):
+                if (self.frame_count <= self.min_hits) or (trk.hit_streak >= self.min_hits):
+                    # id+1 as MOT benchmark requires positive
+                    ret.append(np.concatenate((d, [trk.id+1], [trk.cate], [0])).reshape(1,-1)) 
+                if trk.hit_streak == self.min_hits:
+                    # Head Padding (HP): recover the lost steps during initializing the track
+                    for prev_i in range(self.min_hits - 1):
+                        prev_observation = trk.history_observations[-(prev_i+2)]
+                        ret.append((np.concatenate((prev_observation[:4], [trk.id+1], [trk.cate], 
+                            [-(prev_i+1)]))).reshape(1,-1))
+            i -= 1 
+            if (trk.time_since_update > self.max_age):
+                  self.trackers.pop(i)
+        
+        if(len(ret)>0):
+            return np.concatenate(ret)
+        return np.empty((0, 7))
+
+
diff --git a/trackers/hybrid_sort_tracker/kalmanfilter.py b/trackers/hybrid_sort_tracker/kalmanfilter.py
new file mode 100644
index 0000000000000000000000000000000000000000..3f7ae12c08ad38bf3c0ec4f6bd1bcce177b99b53
--- /dev/null
+++ b/trackers/hybrid_sort_tracker/kalmanfilter.py
@@ -0,0 +1,1591 @@
+# -*- coding: utf-8 -*-
+# pylint: disable=invalid-name, too-many-arguments, too-many-branches,
+# pylint: disable=too-many-locals, too-many-instance-attributes, too-many-lines
+
+"""
+This module implements the linear Kalman filter in both an object
+oriented and procedural form. The KalmanFilter class implements
+the filter by storing the various matrices in instance variables,
+minimizing the amount of bookkeeping you have to do.
+All Kalman filters operate with a predict->update cycle. The
+predict step, implemented with the method or function predict(),
+uses the state transition matrix F to predict the state in the next
+time period (epoch). The state is stored as a gaussian (x, P), where
+x is the state (column) vector, and P is its covariance. Covariance
+matrix Q specifies the process covariance. In Bayesian terms, this
+prediction is called the *prior*, which you can think of colloquially
+as the estimate prior to incorporating the measurement.
+The update step, implemented with the method or function `update()`,
+incorporates the measurement z with covariance R, into the state
+estimate (x, P). The class stores the system uncertainty in S,
+the innovation (residual between prediction and measurement in
+measurement space) in y, and the Kalman gain in k. The procedural
+form returns these variables to you. In Bayesian terms this computes
+the *posterior* - the estimate after the information from the
+measurement is incorporated.
+Whether you use the OO form or procedural form is up to you. If
+matrices such as H, R, and F are changing each epoch, you'll probably
+opt to use the procedural form. If they are unchanging, the OO
+form is perhaps easier to use since you won't need to keep track
+of these matrices. This is especially useful if you are implementing
+banks of filters or comparing various KF designs for performance;
+a trivial coding bug could lead to using the wrong sets of matrices.
+This module also offers an implementation of the RTS smoother, and
+other helper functions, such as log likelihood computations.
+The Saver class allows you to easily save the state of the
+KalmanFilter class after every update
+This module expects NumPy arrays for all values that expect
+arrays, although in a few cases, particularly method parameters,
+it will accept types that convert to NumPy arrays, such as lists
+of lists. These exceptions are documented in the method or function.
+Examples
+--------
+The following example constructs a constant velocity kinematic
+filter, filters noisy data, and plots the results. It also demonstrates
+using the Saver class to save the state of the filter at each epoch.
+.. code-block:: Python
+    import matplotlib.pyplot as plt
+    import numpy as np
+    from filterpy.kalman import KalmanFilter
+    from filterpy.common import Q_discrete_white_noise, Saver
+    r_std, q_std = 2., 0.003
+    cv = KalmanFilter(dim_x=2, dim_z=1)
+    cv.x = np.array([[0., 1.]]) # position, velocity
+    cv.F = np.array([[1, dt],[ [0, 1]])
+    cv.R = np.array([[r_std^^2]])
+    f.H = np.array([[1., 0.]])
+    f.P = np.diag([.1^^2, .03^^2)
+    f.Q = Q_discrete_white_noise(2, dt, q_std**2)
+    saver = Saver(cv)
+    for z in range(100):
+        cv.predict()
+        cv.update([z + randn() * r_std])
+        saver.save() # save the filter's state
+    saver.to_array()
+    plt.plot(saver.x[:, 0])
+    # plot all of the priors
+    plt.plot(saver.x_prior[:, 0])
+    # plot mahalanobis distance
+    plt.figure()
+    plt.plot(saver.mahalanobis)
+This code implements the same filter using the procedural form
+    x = np.array([[0., 1.]]) # position, velocity
+    F = np.array([[1, dt],[ [0, 1]])
+    R = np.array([[r_std^^2]])
+    H = np.array([[1., 0.]])
+    P = np.diag([.1^^2, .03^^2)
+    Q = Q_discrete_white_noise(2, dt, q_std**2)
+    for z in range(100):
+        x, P = predict(x, P, F=F, Q=Q)
+        x, P = update(x, P, z=[z + randn() * r_std], R=R, H=H)
+        xs.append(x[0, 0])
+    plt.plot(xs)
+For more examples see the test subdirectory, or refer to the
+book cited below. In it I both teach Kalman filtering from basic
+principles, and teach the use of this library in great detail.
+FilterPy library.
+http://github.com/rlabbe/filterpy
+Documentation at:
+https://filterpy.readthedocs.org
+Supporting book at:
+https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+This is licensed under an MIT license. See the readme.MD file
+for more information.
+Copyright 2014-2018 Roger R Labbe Jr.
+"""
+
+from __future__ import absolute_import, division
+
+from copy import deepcopy
+from math import log, exp, sqrt
+import sys
+import numpy as np
+from numpy import dot, zeros, eye, isscalar, shape
+import numpy.linalg as linalg
+from filterpy.stats import logpdf
+from filterpy.common import pretty_str, reshape_z
+
+
+class KalmanFilterNew(object):
+    """ Implements a Kalman filter. You are responsible for setting the
+    various state variables to reasonable values; the defaults  will
+    not give you a functional filter.
+    For now the best documentation is my free book Kalman and Bayesian
+    Filters in Python [2]_. The test files in this directory also give you a
+    basic idea of use, albeit without much description.
+    In brief, you will first construct this object, specifying the size of
+    the state vector with dim_x and the size of the measurement vector that
+    you will be using with dim_z. These are mostly used to perform size checks
+    when you assign values to the various matrices. For example, if you
+    specified dim_z=2 and then try to assign a 3x3 matrix to R (the
+    measurement noise matrix you will get an assert exception because R
+    should be 2x2. (If for whatever reason you need to alter the size of
+    things midstream just use the underscore version of the matrices to
+    assign directly: your_filter._R = a_3x3_matrix.)
+    After construction the filter will have default matrices created for you,
+    but you must specify the values for each. It’s usually easiest to just
+    overwrite them rather than assign to each element yourself. This will be
+    clearer in the example below. All are of type numpy.array.
+    Examples
+    --------
+    Here is a filter that tracks position and velocity using a sensor that only
+    reads position.
+    First construct the object with the required dimensionality. Here the state
+    (`dim_x`) has 2 coefficients (position and velocity), and the measurement
+    (`dim_z`) has one. In FilterPy `x` is the state, `z` is the measurement.
+    .. code::
+        from filterpy.kalman import KalmanFilter
+        f = KalmanFilter (dim_x=2, dim_z=1)
+    Assign the initial value for the state (position and velocity). You can do this
+    with a two dimensional array like so:
+        .. code::
+            f.x = np.array([[2.],    # position
+                            [0.]])   # velocity
+    or just use a one dimensional array, which I prefer doing.
+    .. code::
+        f.x = np.array([2., 0.])
+    Define the state transition matrix:
+        .. code::
+            f.F = np.array([[1.,1.],
+                            [0.,1.]])
+    Define the measurement function. Here we need to convert a position-velocity
+    vector into just a position vector, so we use:
+        .. code::
+        f.H = np.array([[1., 0.]])
+    Define the state's covariance matrix P. 
+    .. code::
+        f.P = np.array([[1000.,    0.],
+                        [   0., 1000.] ])
+    Now assign the measurement noise. Here the dimension is 1x1, so I can
+    use a scalar
+    .. code::
+        f.R = 5
+    I could have done this instead:
+    .. code::
+        f.R = np.array([[5.]])
+    Note that this must be a 2 dimensional array.
+    Finally, I will assign the process noise. Here I will take advantage of
+    another FilterPy library function:
+    .. code::
+        from filterpy.common import Q_discrete_white_noise
+        f.Q = Q_discrete_white_noise(dim=2, dt=0.1, var=0.13)
+    Now just perform the standard predict/update loop:
+    .. code::
+        while some_condition_is_true:
+            z = get_sensor_reading()
+            f.predict()
+            f.update(z)
+            do_something_with_estimate (f.x)
+    **Procedural Form**
+    This module also contains stand alone functions to perform Kalman filtering.
+    Use these if you are not a fan of objects.
+    **Example**
+    .. code::
+        while True:
+            z, R = read_sensor()
+            x, P = predict(x, P, F, Q)
+            x, P = update(x, P, z, R, H)
+    See my book Kalman and Bayesian Filters in Python [2]_.
+    You will have to set the following attributes after constructing this
+    object for the filter to perform properly. Please note that there are
+    various checks in place to ensure that you have made everything the
+    'correct' size. However, it is possible to provide incorrectly sized
+    arrays such that the linear algebra can not perform an operation.
+    It can also fail silently - you can end up with matrices of a size that
+    allows the linear algebra to work, but are the wrong shape for the problem
+    you are trying to solve.
+    Parameters
+    ----------
+    dim_x : int
+        Number of state variables for the Kalman filter. For example, if
+        you are tracking the position and velocity of an object in two
+        dimensions, dim_x would be 4.
+        This is used to set the default size of P, Q, and u
+    dim_z : int
+        Number of of measurement inputs. For example, if the sensor
+        provides you with position in (x,y), dim_z would be 2.
+    dim_u : int (optional)
+        size of the control input, if it is being used.
+        Default value of 0 indicates it is not used.
+    compute_log_likelihood : bool (default = True)
+        Computes log likelihood by default, but this can be a slow
+        computation, so if you never use it you can turn this computation
+        off.
+    Attributes
+    ----------
+    x : numpy.array(dim_x, 1)
+        Current state estimate. Any call to update() or predict() updates
+        this variable.
+    P : numpy.array(dim_x, dim_x)
+        Current state covariance matrix. Any call to update() or predict()
+        updates this variable.
+    x_prior : numpy.array(dim_x, 1)
+        Prior (predicted) state estimate. The *_prior and *_post attributes
+        are for convenience; they store the  prior and posterior of the
+        current epoch. Read Only.
+    P_prior : numpy.array(dim_x, dim_x)
+        Prior (predicted) state covariance matrix. Read Only.
+    x_post : numpy.array(dim_x, 1)
+        Posterior (updated) state estimate. Read Only.
+    P_post : numpy.array(dim_x, dim_x)
+        Posterior (updated) state covariance matrix. Read Only.
+    z : numpy.array
+        Last measurement used in update(). Read only.
+    R : numpy.array(dim_z, dim_z)
+        Measurement noise covariance matrix. Also known as the
+        observation covariance.
+    Q : numpy.array(dim_x, dim_x)
+        Process noise covariance matrix. Also known as the transition
+        covariance.
+    F : numpy.array()
+        State Transition matrix. Also known as `A` in some formulation.
+    H : numpy.array(dim_z, dim_x)
+        Measurement function. Also known as the observation matrix, or as `C`.
+    y : numpy.array
+        Residual of the update step. Read only.
+    K : numpy.array(dim_x, dim_z)
+        Kalman gain of the update step. Read only.
+    S :  numpy.array
+        System uncertainty (P projected to measurement space). Read only.
+    SI :  numpy.array
+        Inverse system uncertainty. Read only.
+    log_likelihood : float
+        log-likelihood of the last measurement. Read only.
+    likelihood : float
+        likelihood of last measurement. Read only.
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+    mahalanobis : float
+        mahalanobis distance of the innovation. Read only.
+    inv : function, default numpy.linalg.inv
+        If you prefer another inverse function, such as the Moore-Penrose
+        pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        This is only used to invert self.S. If you know it is diagonal, you
+        might choose to set it to filterpy.common.inv_diagonal, which is
+        several times faster than numpy.linalg.inv for diagonal matrices.
+    alpha : float
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+    References
+    ----------
+    .. [1] Dan Simon. "Optimal State Estimation." John Wiley & Sons.
+       p. 208-212. (2006)
+    .. [2] Roger Labbe. "Kalman and Bayesian Filters in Python"
+       https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+    """
+
+    def __init__(self, dim_x, dim_z, dim_u=0, args=None):
+        if dim_x < 1:
+            raise ValueError('dim_x must be 1 or greater')
+        if dim_z < 1:
+            raise ValueError('dim_z must be 1 or greater')
+        if dim_u < 0:
+            raise ValueError('dim_u must be 0 or greater')
+
+        self.dim_x = dim_x
+        self.dim_z = dim_z
+        self.dim_u = dim_u
+
+        self.x = zeros((dim_x, 1))        # state
+        self.P = eye(dim_x)               # uncertainty covariance
+        self.Q = eye(dim_x)               # process uncertainty
+        self.B = None                     # control transition matrix
+        self.F = eye(dim_x)               # state transition matrix
+        self.H = zeros((dim_z, dim_x))    # measurement function
+        self.R = eye(dim_z)               # measurement uncertainty
+        self._alpha_sq = 1.               # fading memory control
+        self.M = np.zeros((dim_x, dim_z)) # process-measurement cross correlation
+        self.z = np.array([[None]*self.dim_z]).T
+
+        # gain and residual are computed during the innovation step. We
+        # save them so that in case you want to inspect them for various
+        # purposes
+        self.K = np.zeros((dim_x, dim_z)) # kalman gain
+        self.y = zeros((dim_z, 1))
+        self.S = np.zeros((dim_z, dim_z)) # system uncertainty
+        self.SI = np.zeros((dim_z, dim_z)) # inverse system uncertainty
+
+        # identity matrix. Do not alter this.
+        self._I = np.eye(dim_x)
+
+        # these will always be a copy of x,P after predict() is called
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+        # these will always be a copy of x,P after update() is called
+        self.x_post = self.x.copy()             
+        self.P_post = self.P.copy()
+
+        # Only computed only if requested via property
+        self._log_likelihood = log(sys.float_info.min)
+        self._likelihood = sys.float_info.min
+        self._mahalanobis = None
+
+        # keep all observations 
+        self.history_obs = []
+
+        self.inv = np.linalg.inv
+
+        self.attr_saved = None
+        self.observed = False
+        self.args = args
+
+
+    def predict(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            self.x = dot(F, self.x) + dot(B, u)
+        else:
+            self.x = dot(F, self.x)
+
+        # P = FPF' + Q
+        self.P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+
+
+    def freeze(self):
+        """
+            Save the parameters before non-observation forward
+        """
+        self.attr_saved = deepcopy(self.__dict__)
+
+
+    def unfreeze(self):
+        if self.attr_saved is not None:
+            new_history = deepcopy(self.history_obs)
+            self.__dict__ = self.attr_saved
+            # self.history_obs = new_history 
+            self.history_obs = self.history_obs[:-1]
+            occur = [int(d is None) for d in new_history]
+            indices = np.where(np.array(occur)==0)[0]
+            index1 = indices[-2]
+            index2 = indices[-1]
+            box1 = new_history[index1]
+            x1, y1, s1, r1 = box1 
+            w1 = np.sqrt(s1 * r1)
+            h1 = np.sqrt(s1 / r1)
+            box2 = new_history[index2]
+            x2, y2, s2, r2 = box2 
+            w2 = np.sqrt(s2 * r2)
+            h2 = np.sqrt(s2 / r2)
+            time_gap = index2 - index1
+            dx = (x2-x1)/time_gap
+            dy = (y2-y1)/time_gap 
+            dw = (w2-w1)/time_gap 
+            dh = (h2-h1)/time_gap
+            for i in range(index2 - index1):
+                """
+                    The default virtual trajectory generation is by linear
+                    motion (constant speed hypothesis), you could modify this 
+                    part to implement your own. 
+                """
+                x = x1 + (i+1) * dx 
+                y = y1 + (i+1) * dy 
+                w = w1 + (i+1) * dw 
+                h = h1 + (i+1) * dh
+                s = w * h 
+                r = w / float(h)
+                new_box = np.array([x, y, s, r]).reshape((4, 1))
+                """
+                    I still use predict-update loop here to refresh the parameters,
+                    but this can be faster by directly modifying the internal parameters
+                    as suggested in the paper. I keep this naive but slow way for 
+                    easy read and understanding
+                """
+
+                if not i == (index2-index1-1):
+                    self.update(new_box)
+                    self.predict()
+                else:
+                    self.update(new_box)
+
+
+    def update(self, z, R=None, H=None):
+        """
+        Add a new measurement (z) to the Kalman filter.
+        If z is None, nothing is computed. However, x_post and P_post are
+        updated with the prior (x_prior, P_prior), and self.z is set to None.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+            If you pass in a value of H, z must be a column vector the
+            of the correct size.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array, or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise self.H will be used.
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        # append the observation
+        self.history_obs.append(z)
+        
+        if z is None:
+            if self.observed:
+                """
+                    Got no observation so freeze the current parameters for future
+                    potential online smoothing.
+                """
+                self.freeze()
+            self.observed = False 
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+        
+        # self.observed = True
+        if not self.observed:
+            """
+                Get observation, use online smoothing to re-update parameters
+            """
+            self.unfreeze()
+        self.observed = True
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        # if self.args.use_nsa_kalman:
+        #     if confidence > 0.6:
+        #         R = [(1 - confidence) * self.args.nsa_kalman_interval * x for x in R]
+        #     else:
+        #         R = [self.args.nsa_kalman_interval_sec * x for x in R]
+
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # S = HPH' + R
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + R
+        self.SI = self.inv(self.S)
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        # This is more numerically stable
+        # and works for non-optimal K vs the equation
+        # P = (I-KH)P usually seen in the literature.
+
+        I_KH = self._I - dot(self.K, H)
+        self.P = dot(dot(I_KH, self.P), I_KH.T) + dot(dot(self.K, R), self.K.T)
+
+        # save measurement and posterior state
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def predict_steadystate(self, u=0, B=None):
+        """
+        Predict state (prior) using the Kalman filter state propagation
+        equations. Only x is updated, P is left unchanged. See
+        update_steadstate() for a longer explanation of when to use this
+        method.
+        Parameters
+        ----------
+        u : np.array
+            Optional control vector. If non-zero, it is multiplied by B
+            to create the control input into the system.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        """
+
+        if B is None:
+            B = self.B
+
+        # x = Fx + Bu
+        if B is not None:
+            self.x = dot(self.F, self.x) + dot(B, u)
+        else:
+            self.x = dot(self.F, self.x)
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+    def update_steadystate(self, z):
+        """
+        Add a new measurement (z) to the Kalman filter without recomputing
+        the Kalman gain K, the state covariance P, or the system
+        uncertainty S.
+        You can use this for LTI systems since the Kalman gain and covariance
+        converge to a fixed value. Precompute these and assign them explicitly,
+        or run the Kalman filter using the normal predict()/update(0 cycle
+        until they converge.
+        The main advantage of this call is speed. We do significantly less
+        computation, notably avoiding a costly matrix inversion.
+        Use in conjunction with predict_steadystate(), otherwise P will grow
+        without bound.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Examples
+        --------
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> # let filter converge on representative data, then save k and P
+        >>> for i in range(100):
+        >>>     cv.predict()
+        >>>     cv.update([i, i, i])
+        >>> saved_k = np.copy(cv.K)
+        >>> saved_P = np.copy(cv.P)
+        later on:
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> cv.K = np.copy(saved_K)
+        >>> cv.P = np.copy(saved_P)
+        >>> for i in range(100):
+        >>>     cv.predict_steadystate()
+        >>>     cv.update_steadystate([i, i, i])
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(self.H, self.x)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+    def update_correlated(self, z, R=None, H=None):
+        """ Add a new measurement (z) to the Kalman filter assuming that
+        process noise and measurement noise are correlated as defined in
+        the `self.M` matrix.
+        A partial derivation can be found in [1]
+        If z is None, nothing is changed.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array,  or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise  self.H will be used.
+        References
+        ----------
+        .. [1] Bulut, Y. (2011). Applied Kalman filter theory (Doctoral dissertation, Northeastern University).
+               http://people.duke.edu/~hpgavin/SystemID/References/Balut-KalmanFilter-PhD-NEU-2011.pdf
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        # rename for readability and a tiny extra bit of speed
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # handle special case: if z is in form [[z]] but x is not a column
+        # vector dimensions will not match
+        if self.x.ndim == 1 and shape(z) == (1, 1):
+            z = z[0]
+
+        if shape(z) == (): # is it scalar, e.g. z=3 or z=np.array(3)
+            z = np.asarray([z])
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + dot(H, self.M) + dot(self.M.T, H.T) + R
+        self.SI = self.inv(self.S)
+
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT + self.M, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+        self.P = self.P - dot(self.K, dot(H, self.P) + self.M.T)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def batch_filter(self, zs, Fs=None, Qs=None, Hs=None,
+                     Rs=None, Bs=None, us=None, update_first=False,
+                     saver=None):
+        """ Batch processes a sequences of measurements.
+        Parameters
+        ----------
+        zs : list-like
+            list of measurements at each time step `self.dt`. Missing
+            measurements must be represented by `None`.
+        Fs : None, list-like, default=None
+            optional value or list of values to use for the state transition
+            matrix F.
+            If Fs is None then self.F is used for all epochs.
+            Otherwise it must contain a list-like list of F's, one for
+            each epoch.  This allows you to have varying F per epoch.
+        Qs : None, np.array or list-like, default=None
+            optional value or list of values to use for the process error
+            covariance Q.
+            If Qs is None then self.Q is used for all epochs.
+            Otherwise it must contain a list-like list of Q's, one for
+            each epoch.  This allows you to have varying Q per epoch.
+        Hs : None, np.array or list-like, default=None
+            optional list of values to use for the measurement matrix H.
+            If Hs is None then self.H is used for all epochs.
+            If Hs contains a single matrix, then it is used as H for all
+            epochs.
+            Otherwise it must contain a list-like list of H's, one for
+            each epoch.  This allows you to have varying H per epoch.
+        Rs : None, np.array or list-like, default=None
+            optional list of values to use for the measurement error
+            covariance R.
+            If Rs is None then self.R is used for all epochs.
+            Otherwise it must contain a list-like list of R's, one for
+            each epoch.  This allows you to have varying R per epoch.
+        Bs : None, np.array or list-like, default=None
+            optional list of values to use for the control transition matrix B.
+            If Bs is None then self.B is used for all epochs.
+            Otherwise it must contain a list-like list of B's, one for
+            each epoch.  This allows you to have varying B per epoch.
+        us : None, np.array or list-like, default=None
+            optional list of values to use for the control input vector;
+            If us is None then None is used for all epochs (equivalent to 0,
+            or no control input).
+            Otherwise it must contain a list-like list of u's, one for
+            each epoch.
+       update_first : bool, optional, default=False
+            controls whether the order of operations is update followed by
+            predict, or predict followed by update. Default is predict->update.
+        saver : filterpy.common.Saver, optional
+            filterpy.common.Saver object. If provided, saver.save() will be
+            called after every epoch
+        Returns
+        -------
+        means : np.array((n,dim_x,1))
+            array of the state for each time step after the update. Each entry
+            is an np.array. In other words `means[k,:]` is the state at step
+            `k`.
+        covariance : np.array((n,dim_x,dim_x))
+            array of the covariances for each time step after the update.
+            In other words `covariance[k,:,:]` is the covariance at step `k`.
+        means_predictions : np.array((n,dim_x,1))
+            array of the state for each time step after the predictions. Each
+            entry is an np.array. In other words `means[k,:]` is the state at
+            step `k`.
+        covariance_predictions : np.array((n,dim_x,dim_x))
+            array of the covariances for each time step after the prediction.
+            In other words `covariance[k,:,:]` is the covariance at step `k`.
+        Examples
+        --------
+        .. code-block:: Python
+            # this example demonstrates tracking a measurement where the time
+            # between measurement varies, as stored in dts. This requires
+            # that F be recomputed for each epoch. The output is then smoothed
+            # with an RTS smoother.
+            zs = [t + random.randn()*4 for t in range (40)]
+            Fs = [np.array([[1., dt], [0, 1]] for dt in dts]
+            (mu, cov, _, _) = kf.batch_filter(zs, Fs=Fs)
+            (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs)
+        """
+
+        #pylint: disable=too-many-statements
+        n = np.size(zs, 0)
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+        if Hs is None:
+            Hs = [self.H] * n
+        if Rs is None:
+            Rs = [self.R] * n
+        if Bs is None:
+            Bs = [self.B] * n
+        if us is None:
+            us = [0] * n
+
+        # mean estimates from Kalman Filter
+        if self.x.ndim == 1:
+            means = zeros((n, self.dim_x))
+            means_p = zeros((n, self.dim_x))
+        else:
+            means = zeros((n, self.dim_x, 1))
+            means_p = zeros((n, self.dim_x, 1))
+
+        # state covariances from Kalman Filter
+        covariances = zeros((n, self.dim_x, self.dim_x))
+        covariances_p = zeros((n, self.dim_x, self.dim_x))
+
+        if update_first:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+        else:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+
+        return (means, covariances, means_p, covariances_p)
+
+    def rts_smoother(self, Xs, Ps, Fs=None, Qs=None, inv=np.linalg.inv):
+        """
+        Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+        means and covariances computed by a Kalman filter. The usual input
+        would come from the output of `KalmanFilter.batch_filter()`.
+        Parameters
+        ----------
+        Xs : numpy.array
+           array of the means (state variable x) of the output of a Kalman
+           filter.
+        Ps : numpy.array
+            array of the covariances of the output of a kalman filter.
+        Fs : list-like collection of numpy.array, optional
+            State transition matrix of the Kalman filter at each time step.
+            Optional, if not provided the filter's self.F will be used
+        Qs : list-like collection of numpy.array, optional
+            Process noise of the Kalman filter at each time step. Optional,
+            if not provided the filter's self.Q will be used
+        inv : function, default numpy.linalg.inv
+            If you prefer another inverse function, such as the Moore-Penrose
+            pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        Returns
+        -------
+        x : numpy.ndarray
+           smoothed means
+        P : numpy.ndarray
+           smoothed state covariances
+        K : numpy.ndarray
+            smoother gain at each step
+        Pp : numpy.ndarray
+           Predicted state covariances
+        Examples
+        --------
+        .. code-block:: Python
+            zs = [t + random.randn()*4 for t in range (40)]
+            (mu, cov, _, _) = kalman.batch_filter(zs)
+            (x, P, K, Pp) = rts_smoother(mu, cov, kf.F, kf.Q)
+        """
+
+        if len(Xs) != len(Ps):
+            raise ValueError('length of Xs and Ps must be the same')
+
+        n = Xs.shape[0]
+        dim_x = Xs.shape[1]
+
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+
+        # smoother gain
+        K = zeros((n, dim_x, dim_x))
+
+        x, P, Pp = Xs.copy(), Ps.copy(), Ps.copy()
+        for k in range(n-2, -1, -1):
+            Pp[k] = dot(dot(Fs[k+1], P[k]), Fs[k+1].T) + Qs[k+1]
+
+            #pylint: disable=bad-whitespace
+            K[k]  = dot(dot(P[k], Fs[k+1].T), inv(Pp[k]))
+            x[k] += dot(K[k], x[k+1] - dot(Fs[k+1], x[k]))
+            P[k] += dot(dot(K[k], P[k+1] - Pp[k]), K[k].T)
+
+        return (x, P, K, Pp)
+
+    def get_prediction(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations and returns it without modifying the object.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the prediction.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            x = dot(F, self.x) + dot(B, u)
+        else:
+            x = dot(F, self.x)
+
+        # P = FPF' + Q
+        P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        return x, P
+
+    def get_update(self, z=None):
+        """
+        Computes the new estimate based on measurement `z` and returns it
+        without altering the state of the filter.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the update.
+       """
+
+        if z is None:
+            return self.x, self.P
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        R = self.R
+        H = self.H
+        P = self.P
+        x = self.x
+
+        # error (residual) between measurement and prediction
+        y = z - dot(H, x)
+
+        # common subexpression for speed
+        PHT = dot(P, H.T)
+
+        # project system uncertainty into measurement space
+        S = dot(H, PHT) + R
+
+        # map system uncertainty into kalman gain
+        K = dot(PHT, self.inv(S))
+
+        # predict new x with residual scaled by the kalman gain
+        x = x + dot(K, y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        I_KH = self._I - dot(K, H)
+        P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+        return x, P
+
+    def residual_of(self, z):
+        """
+        Returns the residual for the given measurement (z). Does not alter
+        the state of the filter.
+        """
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+        return z - dot(self.H, self.x_prior)
+
+    def measurement_of_state(self, x):
+        """
+        Helper function that converts a state into a measurement.
+        Parameters
+        ----------
+        x : np.array
+            kalman state vector
+        Returns
+        -------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        """
+
+        return dot(self.H, x)
+
+    @property
+    def log_likelihood(self):
+        """
+        log-likelihood of the last measurement.
+        """
+        if self._log_likelihood is None:
+            self._log_likelihood = logpdf(x=self.y, cov=self.S)
+        return self._log_likelihood
+
+    @property
+    def likelihood(self):
+        """
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+        """
+        if self._likelihood is None:
+            self._likelihood = exp(self.log_likelihood)
+            if self._likelihood == 0:
+                self._likelihood = sys.float_info.min
+        return self._likelihood
+
+    @property
+    def mahalanobis(self):
+        """"
+        Mahalanobis distance of measurement. E.g. 3 means measurement
+        was 3 standard deviations away from the predicted value.
+        Returns
+        -------
+        mahalanobis : float
+        """
+        if self._mahalanobis is None:
+            self._mahalanobis = sqrt(float(dot(dot(self.y.T, self.SI), self.y)))
+        return self._mahalanobis
+
+    @property
+    def alpha(self):
+        """
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+        """
+        return self._alpha_sq**.5
+
+    def log_likelihood_of(self, z):
+        """
+        log likelihood of the measurement `z`. This should only be called
+        after a call to update(). Calling after predict() will yield an
+        incorrect result."""
+
+        if z is None:
+            return log(sys.float_info.min)
+        return logpdf(z, dot(self.H, self.x), self.S)
+
+    @alpha.setter
+    def alpha(self, value):
+        if not np.isscalar(value) or value < 1:
+            raise ValueError('alpha must be a float greater than 1')
+
+        self._alpha_sq = value**2
+
+    def __repr__(self):
+        return '\n'.join([
+            'KalmanFilter object',
+            pretty_str('dim_x', self.dim_x),
+            pretty_str('dim_z', self.dim_z),
+            pretty_str('dim_u', self.dim_u),
+            pretty_str('x', self.x),
+            pretty_str('P', self.P),
+            pretty_str('x_prior', self.x_prior),
+            pretty_str('P_prior', self.P_prior),
+            pretty_str('x_post', self.x_post),
+            pretty_str('P_post', self.P_post),
+            pretty_str('F', self.F),
+            pretty_str('Q', self.Q),
+            pretty_str('R', self.R),
+            pretty_str('H', self.H),
+            pretty_str('K', self.K),
+            pretty_str('y', self.y),
+            pretty_str('S', self.S),
+            pretty_str('SI', self.SI),
+            pretty_str('M', self.M),
+            pretty_str('B', self.B),
+            pretty_str('z', self.z),
+            pretty_str('log-likelihood', self.log_likelihood),
+            pretty_str('likelihood', self.likelihood),
+            pretty_str('mahalanobis', self.mahalanobis),
+            pretty_str('alpha', self.alpha),
+            pretty_str('inv', self.inv)
+            ])
+
+    def test_matrix_dimensions(self, z=None, H=None, R=None, F=None, Q=None):
+        """
+        Performs a series of asserts to check that the size of everything
+        is what it should be. This can help you debug problems in your design.
+        If you pass in H, R, F, Q those will be used instead of this object's
+        value for those matrices.
+        Testing `z` (the measurement) is problamatic. x is a vector, and can be
+        implemented as either a 1D array or as a nx1 column vector. Thus Hx
+        can be of different shapes. Then, if Hx is a single value, it can
+        be either a 1D array or 2D vector. If either is true, z can reasonably
+        be a scalar (either '3' or np.array('3') are scalars under this
+        definition), a 1D, 1 element array, or a 2D, 1 element array. You are
+        allowed to pass in any combination that works.
+        """
+
+        if H is None:
+            H = self.H
+        if R is None:
+            R = self.R
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        x = self.x
+        P = self.P
+
+        assert x.ndim == 1 or x.ndim == 2, \
+                "x must have one or two dimensions, but has {}".format(x.ndim)
+
+        if x.ndim == 1:
+            assert x.shape[0] == self.dim_x, \
+                   "Shape of x must be ({},{}), but is {}".format(
+                       self.dim_x, 1, x.shape)
+        else:
+            assert x.shape == (self.dim_x, 1), \
+                   "Shape of x must be ({},{}), but is {}".format(
+                       self.dim_x, 1, x.shape)
+
+        assert P.shape == (self.dim_x, self.dim_x), \
+               "Shape of P must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, P.shape)
+
+        assert Q.shape == (self.dim_x, self.dim_x), \
+               "Shape of Q must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, P.shape)
+
+        assert F.shape == (self.dim_x, self.dim_x), \
+               "Shape of F must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, F.shape)
+
+        assert np.ndim(H) == 2, \
+               "Shape of H must be (dim_z, {}), but is {}".format(
+                   P.shape[0], shape(H))
+
+        assert H.shape[1] == P.shape[0], \
+               "Shape of H must be (dim_z, {}), but is {}".format(
+                   P.shape[0], H.shape)
+
+        # shape of R must be the same as HPH'
+        hph_shape = (H.shape[0], H.shape[0])
+        r_shape = shape(R)
+
+        if H.shape[0] == 1:
+            # r can be scalar, 1D, or 2D in this case
+            assert r_shape in [(), (1,), (1, 1)], \
+            "R must be scalar or one element array, but is shaped {}".format(
+                r_shape)
+        else:
+            assert r_shape == hph_shape, \
+            "shape of R should be {} but it is {}".format(hph_shape, r_shape)
+
+
+        if z is not None:
+            z_shape = shape(z)
+        else:
+            z_shape = (self.dim_z, 1)
+
+        # H@x must have shape of z
+        Hx = dot(H, x)
+
+        if z_shape == (): # scalar or np.array(scalar)
+            assert Hx.ndim == 1 or shape(Hx) == (1, 1), \
+            "shape of z should be {}, not {} for the given H".format(
+                shape(Hx), z_shape)
+
+        elif shape(Hx) == (1,):
+            assert z_shape[0] == 1, 'Shape of z must be {} for the given H'.format(shape(Hx))
+
+        else:
+            assert (z_shape == shape(Hx) or
+                    (len(z_shape) == 1 and shape(Hx) == (z_shape[0], 1))), \
+                    "shape of z should be {}, not {} for the given H".format(
+                        shape(Hx), z_shape)
+
+        if np.ndim(Hx) > 1 and shape(Hx) != (1, 1):
+            assert shape(Hx) == z_shape, \
+               'shape of z should be {} for the given H, but it is {}'.format(
+                   shape(Hx), z_shape)
+
+
+def update(x, P, z, R, H=None, return_all=False):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    update(1, 2, 1, 1, 1)  # univariate
+    update(x, P, 1
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    P : numpy.array(dim_x, dim_x), or float
+        Covariance matrix
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    R : numpy.array(dim_z, dim_z), or float
+        Measurement noise matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    return_all : bool, default False
+        If true, y, K, S, and log_likelihood are returned, otherwise
+        only x and P are returned.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    P : numpy.array
+        Posterior covariance matrix
+    y : numpy.array or scalar
+        Residua. Difference between measurement and state in measurement space
+    K : numpy.array
+        Kalman gain
+    S : numpy.array
+        System uncertainty in measurement space
+    log_likelihood : float
+        log likelihood of the measurement
+    """
+
+    #pylint: disable=bare-except
+
+    if z is None:
+        if return_all:
+            return x, P, None, None, None, None
+        return x, P
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # project system uncertainty into measurement space
+    S = dot(dot(H, P), H.T) + R
+
+
+    # map system uncertainty into kalman gain
+    try:
+        K = dot(dot(P, H.T), linalg.inv(S))
+    except:
+        # can't invert a 1D array, annoyingly
+        K = dot(dot(P, H.T), 1./S)
+
+
+    # predict new x with residual scaled by the kalman gain
+    x = x + dot(K, y)
+
+    # P = (I-KH)P(I-KH)' + KRK'
+    KH = dot(K, H)
+
+    try:
+        I_KH = np.eye(KH.shape[0]) - KH
+    except:
+        I_KH = np.array([1 - KH])
+    P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+
+    if return_all:
+        # compute log likelihood
+        log_likelihood = logpdf(z, dot(H, x), S)
+        return x, P, y, K, S, log_likelihood
+    return x, P
+
+
+def update_steadystate(x, z, K, H=None):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    K : numpy.array, or float
+        Kalman gain matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    Examples
+    --------
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    >>> update_steadystate(1, 2, 1)  # univariate
+    >>> update_steadystate(x, P, z, H)
+    """
+
+
+    if z is None:
+        return x
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # estimate new x with residual scaled by the kalman gain
+    return x + dot(K, y)
+
+
+def predict(x, P, F=1, Q=0, u=0, B=1, alpha=1.):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    Q : numpy.array, Optional
+        Process noise matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    alpha : float, Optional, default=1.0
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    P : numpy.array
+        Prior covariance matrix
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+    P = (alpha * alpha) * dot(dot(F, P), F.T) + Q
+
+    return x, P
+
+
+def predict_steadystate(x, F=1, u=0, B=1):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations. This steady state form only computes x, assuming that the
+    covariance is constant.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+
+    return x
+
+
+
+def batch_filter(x, P, zs, Fs, Qs, Hs, Rs, Bs=None, us=None,
+                 update_first=False, saver=None):
+    """
+    Batch processes a sequences of measurements.
+    Parameters
+    ----------
+    zs : list-like
+        list of measurements at each time step. Missing measurements must be
+        represented by None.
+    Fs : list-like
+        list of values to use for the state transition matrix matrix.
+    Qs : list-like
+        list of values to use for the process error
+        covariance.
+    Hs : list-like
+        list of values to use for the measurement matrix.
+    Rs : list-like
+        list of values to use for the measurement error
+        covariance.
+    Bs : list-like, optional
+        list of values to use for the control transition matrix;
+        a value of None in any position will cause the filter
+        to use `self.B` for that time step.
+    us : list-like, optional
+        list of values to use for the control input vector;
+        a value of None in any position will cause the filter to use
+        0 for that time step.
+    update_first : bool, optional
+        controls whether the order of operations is update followed by
+        predict, or predict followed by update. Default is predict->update.
+        saver : filterpy.common.Saver, optional
+            filterpy.common.Saver object. If provided, saver.save() will be
+            called after every epoch
+    Returns
+    -------
+    means : np.array((n,dim_x,1))
+        array of the state for each time step after the update. Each entry
+        is an np.array. In other words `means[k,:]` is the state at step
+        `k`.
+    covariance : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the update.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    means_predictions : np.array((n,dim_x,1))
+        array of the state for each time step after the predictions. Each
+        entry is an np.array. In other words `means[k,:]` is the state at
+        step `k`.
+    covariance_predictions : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the prediction.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        Fs = [kf.F for t in range (40)]
+        Hs = [kf.H for t in range (40)]
+        (mu, cov, _, _) = kf.batch_filter(zs, Rs=R_list, Fs=Fs, Hs=Hs, Qs=None,
+                                          Bs=None, us=None, update_first=False)
+        (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs, Qs=None)
+    """
+
+    n = np.size(zs, 0)
+    dim_x = x.shape[0]
+
+    # mean estimates from Kalman Filter
+    if x.ndim == 1:
+        means = zeros((n, dim_x))
+        means_p = zeros((n, dim_x))
+    else:
+        means = zeros((n, dim_x, 1))
+        means_p = zeros((n, dim_x, 1))
+
+    # state covariances from Kalman Filter
+    covariances = zeros((n, dim_x, dim_x))
+    covariances_p = zeros((n, dim_x, dim_x))
+
+    if us is None:
+        us = [0.] * n
+        Bs = [0.] * n
+
+    if update_first:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+            if saver is not None:
+                saver.save()
+    else:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+            if saver is not None:
+                saver.save()
+
+    return (means, covariances, means_p, covariances_p)
+
+
+
+def rts_smoother(Xs, Ps, Fs, Qs):
+    """
+    Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+    means and covariances computed by a Kalman filter. The usual input
+    would come from the output of `KalmanFilter.batch_filter()`.
+    Parameters
+    ----------
+    Xs : numpy.array
+       array of the means (state variable x) of the output of a Kalman
+       filter.
+    Ps : numpy.array
+        array of the covariances of the output of a kalman filter.
+    Fs : list-like collection of numpy.array
+        State transition matrix of the Kalman filter at each time step.
+    Qs : list-like collection of numpy.array, optional
+        Process noise of the Kalman filter at each time step.
+    Returns
+    -------
+    x : numpy.ndarray
+       smoothed means
+    P : numpy.ndarray
+       smoothed state covariances
+    K : numpy.ndarray
+        smoother gain at each step
+    pP : numpy.ndarray
+       predicted state covariances
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        (mu, cov, _, _) = kalman.batch_filter(zs)
+        (x, P, K, pP) = rts_smoother(mu, cov, kf.F, kf.Q)
+    """
+
+    if len(Xs) != len(Ps):
+        raise ValueError('length of Xs and Ps must be the same')
+
+    n = Xs.shape[0]
+    dim_x = Xs.shape[1]
+
+    # smoother gain
+    K = zeros((n, dim_x, dim_x))
+    x, P, pP = Xs.copy(), Ps.copy(), Ps.copy()
+
+    for k in range(n-2, -1, -1):
+        pP[k] = dot(dot(Fs[k], P[k]), Fs[k].T) + Qs[k]
+
+        #pylint: disable=bad-whitespace
+        K[k]  = dot(dot(P[k], Fs[k].T), linalg.inv(pP[k]))
+        x[k] += dot(K[k], x[k+1] - dot(Fs[k], x[k]))
+        P[k] += dot(dot(K[k], P[k+1] - pP[k]), K[k].T)
+
+    return (x, P, K, pP)
\ No newline at end of file
diff --git a/trackers/hybrid_sort_tracker/kalmanfilter_score.py b/trackers/hybrid_sort_tracker/kalmanfilter_score.py
new file mode 100644
index 0000000000000000000000000000000000000000..64d00b91f5333825d5168cf682c9a7203de36fd0
--- /dev/null
+++ b/trackers/hybrid_sort_tracker/kalmanfilter_score.py
@@ -0,0 +1,1586 @@
+# -*- coding: utf-8 -*-
+# pylint: disable=invalid-name, too-many-arguments, too-many-branches,
+# pylint: disable=too-many-locals, too-many-instance-attributes, too-many-lines
+
+"""
+This module implements the linear Kalman filter in both an object
+oriented and procedural form. The KalmanFilter class implements
+the filter by storing the various matrices in instance variables,
+minimizing the amount of bookkeeping you have to do.
+All Kalman filters operate with a predict->update cycle. The
+predict step, implemented with the method or function predict(),
+uses the state transition matrix F to predict the state in the next
+time period (epoch). The state is stored as a gaussian (x, P), where
+x is the state (column) vector, and P is its covariance. Covariance
+matrix Q specifies the process covariance. In Bayesian terms, this
+prediction is called the *prior*, which you can think of colloquially
+as the estimate prior to incorporating the measurement.
+The update step, implemented with the method or function `update()`,
+incorporates the measurement z with covariance R, into the state
+estimate (x, P). The class stores the system uncertainty in S,
+the innovation (residual between prediction and measurement in
+measurement space) in y, and the Kalman gain in k. The procedural
+form returns these variables to you. In Bayesian terms this computes
+the *posterior* - the estimate after the information from the
+measurement is incorporated.
+Whether you use the OO form or procedural form is up to you. If
+matrices such as H, R, and F are changing each epoch, you'll probably
+opt to use the procedural form. If they are unchanging, the OO
+form is perhaps easier to use since you won't need to keep track
+of these matrices. This is especially useful if you are implementing
+banks of filters or comparing various KF designs for performance;
+a trivial coding bug could lead to using the wrong sets of matrices.
+This module also offers an implementation of the RTS smoother, and
+other helper functions, such as log likelihood computations.
+The Saver class allows you to easily save the state of the
+KalmanFilter class after every update
+This module expects NumPy arrays for all values that expect
+arrays, although in a few cases, particularly method parameters,
+it will accept types that convert to NumPy arrays, such as lists
+of lists. These exceptions are documented in the method or function.
+Examples
+--------
+The following example constructs a constant velocity kinematic
+filter, filters noisy data, and plots the results. It also demonstrates
+using the Saver class to save the state of the filter at each epoch.
+.. code-block:: Python
+    import matplotlib.pyplot as plt
+    import numpy as np
+    from filterpy.kalman import KalmanFilter
+    from filterpy.common import Q_discrete_white_noise, Saver
+    r_std, q_std = 2., 0.003
+    cv = KalmanFilter(dim_x=2, dim_z=1)
+    cv.x = np.array([[0., 1.]]) # position, velocity
+    cv.F = np.array([[1, dt],[ [0, 1]])
+    cv.R = np.array([[r_std^^2]])
+    f.H = np.array([[1., 0.]])
+    f.P = np.diag([.1^^2, .03^^2)
+    f.Q = Q_discrete_white_noise(2, dt, q_std**2)
+    saver = Saver(cv)
+    for z in range(100):
+        cv.predict()
+        cv.update([z + randn() * r_std])
+        saver.save() # save the filter's state
+    saver.to_array()
+    plt.plot(saver.x[:, 0])
+    # plot all of the priors
+    plt.plot(saver.x_prior[:, 0])
+    # plot mahalanobis distance
+    plt.figure()
+    plt.plot(saver.mahalanobis)
+This code implements the same filter using the procedural form
+    x = np.array([[0., 1.]]) # position, velocity
+    F = np.array([[1, dt],[ [0, 1]])
+    R = np.array([[r_std^^2]])
+    H = np.array([[1., 0.]])
+    P = np.diag([.1^^2, .03^^2)
+    Q = Q_discrete_white_noise(2, dt, q_std**2)
+    for z in range(100):
+        x, P = predict(x, P, F=F, Q=Q)
+        x, P = update(x, P, z=[z + randn() * r_std], R=R, H=H)
+        xs.append(x[0, 0])
+    plt.plot(xs)
+For more examples see the test subdirectory, or refer to the
+book cited below. In it I both teach Kalman filtering from basic
+principles, and teach the use of this library in great detail.
+FilterPy library.
+http://github.com/rlabbe/filterpy
+Documentation at:
+https://filterpy.readthedocs.org
+Supporting book at:
+https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+This is licensed under an MIT license. See the readme.MD file
+for more information.
+Copyright 2014-2018 Roger R Labbe Jr.
+"""
+
+from __future__ import absolute_import, division
+
+from copy import deepcopy
+from math import log, exp, sqrt
+import sys
+import numpy as np
+from numpy import dot, zeros, eye, isscalar, shape
+import numpy.linalg as linalg
+from filterpy.stats import logpdf
+from filterpy.common import pretty_str, reshape_z
+
+
+class KalmanFilterNew_score(object):
+    """ Implements a Kalman filter. You are responsible for setting the
+    various state variables to reasonable values; the defaults  will
+    not give you a functional filter.
+    For now the best documentation is my free book Kalman and Bayesian
+    Filters in Python [2]_. The test files in this directory also give you a
+    basic idea of use, albeit without much description.
+    In brief, you will first construct this object, specifying the size of
+    the state vector with dim_x and the size of the measurement vector that
+    you will be using with dim_z. These are mostly used to perform size checks
+    when you assign values to the various matrices. For example, if you
+    specified dim_z=2 and then try to assign a 3x3 matrix to R (the
+    measurement noise matrix you will get an assert exception because R
+    should be 2x2. (If for whatever reason you need to alter the size of
+    things midstream just use the underscore version of the matrices to
+    assign directly: your_filter._R = a_3x3_matrix.)
+    After construction the filter will have default matrices created for you,
+    but you must specify the values for each. It’s usually easiest to just
+    overwrite them rather than assign to each element yourself. This will be
+    clearer in the example below. All are of type numpy.array.
+    Examples
+    --------
+    Here is a filter that tracks position and velocity using a sensor that only
+    reads position.
+    First construct the object with the required dimensionality. Here the state
+    (`dim_x`) has 2 coefficients (position and velocity), and the measurement
+    (`dim_z`) has one. In FilterPy `x` is the state, `z` is the measurement.
+    .. code::
+        from filterpy.kalman import KalmanFilter
+        f = KalmanFilter (dim_x=2, dim_z=1)
+    Assign the initial value for the state (position and velocity). You can do this
+    with a two dimensional array like so:
+        .. code::
+            f.x = np.array([[2.],    # position
+                            [0.]])   # velocity
+    or just use a one dimensional array, which I prefer doing.
+    .. code::
+        f.x = np.array([2., 0.])
+    Define the state transition matrix:
+        .. code::
+            f.F = np.array([[1.,1.],
+                            [0.,1.]])
+    Define the measurement function. Here we need to convert a position-velocity
+    vector into just a position vector, so we use:
+        .. code::
+        f.H = np.array([[1., 0.]])
+    Define the state's covariance matrix P. 
+    .. code::
+        f.P = np.array([[1000.,    0.],
+                        [   0., 1000.] ])
+    Now assign the measurement noise. Here the dimension is 1x1, so I can
+    use a scalar
+    .. code::
+        f.R = 5
+    I could have done this instead:
+    .. code::
+        f.R = np.array([[5.]])
+    Note that this must be a 2 dimensional array.
+    Finally, I will assign the process noise. Here I will take advantage of
+    another FilterPy library function:
+    .. code::
+        from filterpy.common import Q_discrete_white_noise
+        f.Q = Q_discrete_white_noise(dim=2, dt=0.1, var=0.13)
+    Now just perform the standard predict/update loop:
+    .. code::
+        while some_condition_is_true:
+            z = get_sensor_reading()
+            f.predict()
+            f.update(z)
+            do_something_with_estimate (f.x)
+    **Procedural Form**
+    This module also contains stand alone functions to perform Kalman filtering.
+    Use these if you are not a fan of objects.
+    **Example**
+    .. code::
+        while True:
+            z, R = read_sensor()
+            x, P = predict(x, P, F, Q)
+            x, P = update(x, P, z, R, H)
+    See my book Kalman and Bayesian Filters in Python [2]_.
+    You will have to set the following attributes after constructing this
+    object for the filter to perform properly. Please note that there are
+    various checks in place to ensure that you have made everything the
+    'correct' size. However, it is possible to provide incorrectly sized
+    arrays such that the linear algebra can not perform an operation.
+    It can also fail silently - you can end up with matrices of a size that
+    allows the linear algebra to work, but are the wrong shape for the problem
+    you are trying to solve.
+    Parameters
+    ----------
+    dim_x : int
+        Number of state variables for the Kalman filter. For example, if
+        you are tracking the position and velocity of an object in two
+        dimensions, dim_x would be 4.
+        This is used to set the default size of P, Q, and u
+    dim_z : int
+        Number of of measurement inputs. For example, if the sensor
+        provides you with position in (x,y), dim_z would be 2.
+    dim_u : int (optional)
+        size of the control input, if it is being used.
+        Default value of 0 indicates it is not used.
+    compute_log_likelihood : bool (default = True)
+        Computes log likelihood by default, but this can be a slow
+        computation, so if you never use it you can turn this computation
+        off.
+    Attributes
+    ----------
+    x : numpy.array(dim_x, 1)
+        Current state estimate. Any call to update() or predict() updates
+        this variable.
+    P : numpy.array(dim_x, dim_x)
+        Current state covariance matrix. Any call to update() or predict()
+        updates this variable.
+    x_prior : numpy.array(dim_x, 1)
+        Prior (predicted) state estimate. The *_prior and *_post attributes
+        are for convenience; they store the  prior and posterior of the
+        current epoch. Read Only.
+    P_prior : numpy.array(dim_x, dim_x)
+        Prior (predicted) state covariance matrix. Read Only.
+    x_post : numpy.array(dim_x, 1)
+        Posterior (updated) state estimate. Read Only.
+    P_post : numpy.array(dim_x, dim_x)
+        Posterior (updated) state covariance matrix. Read Only.
+    z : numpy.array
+        Last measurement used in update(). Read only.
+    R : numpy.array(dim_z, dim_z)
+        Measurement noise covariance matrix. Also known as the
+        observation covariance.
+    Q : numpy.array(dim_x, dim_x)
+        Process noise covariance matrix. Also known as the transition
+        covariance.
+    F : numpy.array()
+        State Transition matrix. Also known as `A` in some formulation.
+    H : numpy.array(dim_z, dim_x)
+        Measurement function. Also known as the observation matrix, or as `C`.
+    y : numpy.array
+        Residual of the update step. Read only.
+    K : numpy.array(dim_x, dim_z)
+        Kalman gain of the update step. Read only.
+    S :  numpy.array
+        System uncertainty (P projected to measurement space). Read only.
+    SI :  numpy.array
+        Inverse system uncertainty. Read only.
+    log_likelihood : float
+        log-likelihood of the last measurement. Read only.
+    likelihood : float
+        likelihood of last measurement. Read only.
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+    mahalanobis : float
+        mahalanobis distance of the innovation. Read only.
+    inv : function, default numpy.linalg.inv
+        If you prefer another inverse function, such as the Moore-Penrose
+        pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        This is only used to invert self.S. If you know it is diagonal, you
+        might choose to set it to filterpy.common.inv_diagonal, which is
+        several times faster than numpy.linalg.inv for diagonal matrices.
+    alpha : float
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+    References
+    ----------
+    .. [1] Dan Simon. "Optimal State Estimation." John Wiley & Sons.
+       p. 208-212. (2006)
+    .. [2] Roger Labbe. "Kalman and Bayesian Filters in Python"
+       https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+    """
+
+    def __init__(self, dim_x, dim_z, dim_u=0, args=None):
+        if dim_x < 1:
+            raise ValueError('dim_x must be 1 or greater')
+        if dim_z < 1:
+            raise ValueError('dim_z must be 1 or greater')
+        if dim_u < 0:
+            raise ValueError('dim_u must be 0 or greater')
+
+        self.dim_x = dim_x
+        self.dim_z = dim_z
+        self.dim_u = dim_u
+
+        self.x = zeros((dim_x, 1))        # state
+        self.P = eye(dim_x)               # uncertainty covariance
+        self.Q = eye(dim_x)               # process uncertainty
+        self.B = None                     # control transition matrix
+        self.F = eye(dim_x)               # state transition matrix
+        self.H = zeros((dim_z, dim_x))    # measurement function
+        self.R = eye(dim_z)               # measurement uncertainty
+        self._alpha_sq = 1.               # fading memory control
+        self.M = np.zeros((dim_x, dim_z)) # process-measurement cross correlation
+        self.z = np.array([[None]*self.dim_z]).T
+
+        # gain and residual are computed during the innovation step. We
+        # save them so that in case you want to inspect them for various
+        # purposes
+        self.K = np.zeros((dim_x, dim_z)) # kalman gain
+        self.y = zeros((dim_z, 1))
+        self.S = np.zeros((dim_z, dim_z)) # system uncertainty
+        self.SI = np.zeros((dim_z, dim_z)) # inverse system uncertainty
+
+        # identity matrix. Do not alter this.
+        self._I = np.eye(dim_x)
+
+        # these will always be a copy of x,P after predict() is called
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+        # these will always be a copy of x,P after update() is called
+        self.x_post = self.x.copy()             
+        self.P_post = self.P.copy()
+
+        # Only computed only if requested via property
+        self._log_likelihood = log(sys.float_info.min)
+        self._likelihood = sys.float_info.min
+        self._mahalanobis = None
+
+        # keep all observations 
+        self.history_obs = []
+
+        self.inv = np.linalg.inv
+
+        self.attr_saved = None
+        self.observed = False
+        self.args = args
+
+
+    def predict(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            self.x = dot(F, self.x) + dot(B, u)
+        else:
+            self.x = dot(F, self.x)
+
+        # P = FPF' + Q
+        self.P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+
+    def freeze(self):
+        """
+            Save the parameters before non-observation forward
+        """
+        self.attr_saved = deepcopy(self.__dict__)
+
+
+    def unfreeze(self):
+        if self.attr_saved is not None:
+            new_history = deepcopy(self.history_obs)
+            self.__dict__ = self.attr_saved
+            # self.history_obs = new_history 
+            self.history_obs = self.history_obs[:-1]
+            occur = [int(d is None) for d in new_history]
+            indices = np.where(np.array(occur)==0)[0]
+            index1 = indices[-2]
+            index2 = indices[-1]
+            score1 = new_history[index1]
+            # x1, y1, s1, r1 = box1
+            # w1 = np.sqrt(s1 * r1)
+            # h1 = np.sqrt(s1 / r1)
+            score2 = new_history[index2]
+            # x2, y2, s2, r2 = box2
+            # w2 = np.sqrt(s2 * r2)
+            # h2 = np.sqrt(s2 / r2)
+            time_gap = index2 - index1
+            # dx = (x2-x1)/time_gap
+            # dy = (y2-y1)/time_gap
+            # dw = (w2-w1)/time_gap
+            # dh = (h2-h1)/time_gap
+            dscore = (score2 - score1) / time_gap
+            for i in range(index2 - index1):
+                """
+                    The default virtual trajectory generation is by linear
+                    motion (constant speed hypothesis), you could modify this 
+                    part to implement your own. 
+                """
+                # x = x1 + (i+1) * dx
+                # y = y1 + (i+1) * dy
+                # w = w1 + (i+1) * dw
+                # h = h1 + (i+1) * dh
+                # s = w * h
+                # r = w / float(h)
+                score = score1 + (i+1) * dscore
+                new_score = np.array([score]).reshape((1, 1))
+                """
+                    I still use predict-update loop here to refresh the parameters,
+                    but this can be faster by directly modifying the internal parameters
+                    as suggested in the paper. I keep this naive but slow way for 
+                    easy read and understanding
+                """
+                self.update(new_score)
+                if not i == (index2-index1-1):
+                    self.predict()
+
+
+    def update(self, z, R=None, H=None, confidence=0.0):
+        """
+        Add a new measurement (z) to the Kalman filter.
+        If z is None, nothing is computed. However, x_post and P_post are
+        updated with the prior (x_prior, P_prior), and self.z is set to None.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+            If you pass in a value of H, z must be a column vector the
+            of the correct size.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array, or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise self.H will be used.
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        # append the observation
+        self.history_obs.append(z)
+        
+        if z is None:
+            if self.observed:
+                """
+                    Got no observation so freeze the current parameters for future
+                    potential online smoothing.
+                """
+                self.freeze()
+            self.observed = False 
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+        
+        # self.observed = True
+        if not self.observed:
+            """
+                Get observation, use online smoothing to re-update parameters
+            """
+            self.unfreeze()
+        self.observed = True
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        # if self.args.use_nsa_kalman:
+        #     R = [(1 - confidence) * self.args.nsa_kalman_interval * x for x in R]
+
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # S = HPH' + R
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + R
+        self.SI = self.inv(self.S)
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        # This is more numerically stable
+        # and works for non-optimal K vs the equation
+        # P = (I-KH)P usually seen in the literature.
+
+        I_KH = self._I - dot(self.K, H)
+        self.P = dot(dot(I_KH, self.P), I_KH.T) + dot(dot(self.K, R), self.K.T)
+
+        # save measurement and posterior state
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def predict_steadystate(self, u=0, B=None):
+        """
+        Predict state (prior) using the Kalman filter state propagation
+        equations. Only x is updated, P is left unchanged. See
+        update_steadstate() for a longer explanation of when to use this
+        method.
+        Parameters
+        ----------
+        u : np.array
+            Optional control vector. If non-zero, it is multiplied by B
+            to create the control input into the system.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        """
+
+        if B is None:
+            B = self.B
+
+        # x = Fx + Bu
+        if B is not None:
+            self.x = dot(self.F, self.x) + dot(B, u)
+        else:
+            self.x = dot(self.F, self.x)
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+    def update_steadystate(self, z):
+        """
+        Add a new measurement (z) to the Kalman filter without recomputing
+        the Kalman gain K, the state covariance P, or the system
+        uncertainty S.
+        You can use this for LTI systems since the Kalman gain and covariance
+        converge to a fixed value. Precompute these and assign them explicitly,
+        or run the Kalman filter using the normal predict()/update(0 cycle
+        until they converge.
+        The main advantage of this call is speed. We do significantly less
+        computation, notably avoiding a costly matrix inversion.
+        Use in conjunction with predict_steadystate(), otherwise P will grow
+        without bound.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Examples
+        --------
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> # let filter converge on representative data, then save k and P
+        >>> for i in range(100):
+        >>>     cv.predict()
+        >>>     cv.update([i, i, i])
+        >>> saved_k = np.copy(cv.K)
+        >>> saved_P = np.copy(cv.P)
+        later on:
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> cv.K = np.copy(saved_K)
+        >>> cv.P = np.copy(saved_P)
+        >>> for i in range(100):
+        >>>     cv.predict_steadystate()
+        >>>     cv.update_steadystate([i, i, i])
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(self.H, self.x)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+    def update_correlated(self, z, R=None, H=None):
+        """ Add a new measurement (z) to the Kalman filter assuming that
+        process noise and measurement noise are correlated as defined in
+        the `self.M` matrix.
+        A partial derivation can be found in [1]
+        If z is None, nothing is changed.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array,  or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise  self.H will be used.
+        References
+        ----------
+        .. [1] Bulut, Y. (2011). Applied Kalman filter theory (Doctoral dissertation, Northeastern University).
+               http://people.duke.edu/~hpgavin/SystemID/References/Balut-KalmanFilter-PhD-NEU-2011.pdf
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        # rename for readability and a tiny extra bit of speed
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # handle special case: if z is in form [[z]] but x is not a column
+        # vector dimensions will not match
+        if self.x.ndim == 1 and shape(z) == (1, 1):
+            z = z[0]
+
+        if shape(z) == (): # is it scalar, e.g. z=3 or z=np.array(3)
+            z = np.asarray([z])
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + dot(H, self.M) + dot(self.M.T, H.T) + R
+        self.SI = self.inv(self.S)
+
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT + self.M, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+        self.P = self.P - dot(self.K, dot(H, self.P) + self.M.T)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def batch_filter(self, zs, Fs=None, Qs=None, Hs=None,
+                     Rs=None, Bs=None, us=None, update_first=False,
+                     saver=None):
+        """ Batch processes a sequences of measurements.
+        Parameters
+        ----------
+        zs : list-like
+            list of measurements at each time step `self.dt`. Missing
+            measurements must be represented by `None`.
+        Fs : None, list-like, default=None
+            optional value or list of values to use for the state transition
+            matrix F.
+            If Fs is None then self.F is used for all epochs.
+            Otherwise it must contain a list-like list of F's, one for
+            each epoch.  This allows you to have varying F per epoch.
+        Qs : None, np.array or list-like, default=None
+            optional value or list of values to use for the process error
+            covariance Q.
+            If Qs is None then self.Q is used for all epochs.
+            Otherwise it must contain a list-like list of Q's, one for
+            each epoch.  This allows you to have varying Q per epoch.
+        Hs : None, np.array or list-like, default=None
+            optional list of values to use for the measurement matrix H.
+            If Hs is None then self.H is used for all epochs.
+            If Hs contains a single matrix, then it is used as H for all
+            epochs.
+            Otherwise it must contain a list-like list of H's, one for
+            each epoch.  This allows you to have varying H per epoch.
+        Rs : None, np.array or list-like, default=None
+            optional list of values to use for the measurement error
+            covariance R.
+            If Rs is None then self.R is used for all epochs.
+            Otherwise it must contain a list-like list of R's, one for
+            each epoch.  This allows you to have varying R per epoch.
+        Bs : None, np.array or list-like, default=None
+            optional list of values to use for the control transition matrix B.
+            If Bs is None then self.B is used for all epochs.
+            Otherwise it must contain a list-like list of B's, one for
+            each epoch.  This allows you to have varying B per epoch.
+        us : None, np.array or list-like, default=None
+            optional list of values to use for the control input vector;
+            If us is None then None is used for all epochs (equivalent to 0,
+            or no control input).
+            Otherwise it must contain a list-like list of u's, one for
+            each epoch.
+       update_first : bool, optional, default=False
+            controls whether the order of operations is update followed by
+            predict, or predict followed by update. Default is predict->update.
+        saver : filterpy.common.Saver, optional
+            filterpy.common.Saver object. If provided, saver.save() will be
+            called after every epoch
+        Returns
+        -------
+        means : np.array((n,dim_x,1))
+            array of the state for each time step after the update. Each entry
+            is an np.array. In other words `means[k,:]` is the state at step
+            `k`.
+        covariance : np.array((n,dim_x,dim_x))
+            array of the covariances for each time step after the update.
+            In other words `covariance[k,:,:]` is the covariance at step `k`.
+        means_predictions : np.array((n,dim_x,1))
+            array of the state for each time step after the predictions. Each
+            entry is an np.array. In other words `means[k,:]` is the state at
+            step `k`.
+        covariance_predictions : np.array((n,dim_x,dim_x))
+            array of the covariances for each time step after the prediction.
+            In other words `covariance[k,:,:]` is the covariance at step `k`.
+        Examples
+        --------
+        .. code-block:: Python
+            # this example demonstrates tracking a measurement where the time
+            # between measurement varies, as stored in dts. This requires
+            # that F be recomputed for each epoch. The output is then smoothed
+            # with an RTS smoother.
+            zs = [t + random.randn()*4 for t in range (40)]
+            Fs = [np.array([[1., dt], [0, 1]] for dt in dts]
+            (mu, cov, _, _) = kf.batch_filter(zs, Fs=Fs)
+            (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs)
+        """
+
+        #pylint: disable=too-many-statements
+        n = np.size(zs, 0)
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+        if Hs is None:
+            Hs = [self.H] * n
+        if Rs is None:
+            Rs = [self.R] * n
+        if Bs is None:
+            Bs = [self.B] * n
+        if us is None:
+            us = [0] * n
+
+        # mean estimates from Kalman Filter
+        if self.x.ndim == 1:
+            means = zeros((n, self.dim_x))
+            means_p = zeros((n, self.dim_x))
+        else:
+            means = zeros((n, self.dim_x, 1))
+            means_p = zeros((n, self.dim_x, 1))
+
+        # state covariances from Kalman Filter
+        covariances = zeros((n, self.dim_x, self.dim_x))
+        covariances_p = zeros((n, self.dim_x, self.dim_x))
+
+        if update_first:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+        else:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+
+        return (means, covariances, means_p, covariances_p)
+
+    def rts_smoother(self, Xs, Ps, Fs=None, Qs=None, inv=np.linalg.inv):
+        """
+        Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+        means and covariances computed by a Kalman filter. The usual input
+        would come from the output of `KalmanFilter.batch_filter()`.
+        Parameters
+        ----------
+        Xs : numpy.array
+           array of the means (state variable x) of the output of a Kalman
+           filter.
+        Ps : numpy.array
+            array of the covariances of the output of a kalman filter.
+        Fs : list-like collection of numpy.array, optional
+            State transition matrix of the Kalman filter at each time step.
+            Optional, if not provided the filter's self.F will be used
+        Qs : list-like collection of numpy.array, optional
+            Process noise of the Kalman filter at each time step. Optional,
+            if not provided the filter's self.Q will be used
+        inv : function, default numpy.linalg.inv
+            If you prefer another inverse function, such as the Moore-Penrose
+            pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        Returns
+        -------
+        x : numpy.ndarray
+           smoothed means
+        P : numpy.ndarray
+           smoothed state covariances
+        K : numpy.ndarray
+            smoother gain at each step
+        Pp : numpy.ndarray
+           Predicted state covariances
+        Examples
+        --------
+        .. code-block:: Python
+            zs = [t + random.randn()*4 for t in range (40)]
+            (mu, cov, _, _) = kalman.batch_filter(zs)
+            (x, P, K, Pp) = rts_smoother(mu, cov, kf.F, kf.Q)
+        """
+
+        if len(Xs) != len(Ps):
+            raise ValueError('length of Xs and Ps must be the same')
+
+        n = Xs.shape[0]
+        dim_x = Xs.shape[1]
+
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+
+        # smoother gain
+        K = zeros((n, dim_x, dim_x))
+
+        x, P, Pp = Xs.copy(), Ps.copy(), Ps.copy()
+        for k in range(n-2, -1, -1):
+            Pp[k] = dot(dot(Fs[k+1], P[k]), Fs[k+1].T) + Qs[k+1]
+
+            #pylint: disable=bad-whitespace
+            K[k]  = dot(dot(P[k], Fs[k+1].T), inv(Pp[k]))
+            x[k] += dot(K[k], x[k+1] - dot(Fs[k+1], x[k]))
+            P[k] += dot(dot(K[k], P[k+1] - Pp[k]), K[k].T)
+
+        return (x, P, K, Pp)
+
+    def get_prediction(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations and returns it without modifying the object.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the prediction.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            x = dot(F, self.x) + dot(B, u)
+        else:
+            x = dot(F, self.x)
+
+        # P = FPF' + Q
+        P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        return x, P
+
+    def get_update(self, z=None):
+        """
+        Computes the new estimate based on measurement `z` and returns it
+        without altering the state of the filter.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the update.
+       """
+
+        if z is None:
+            return self.x, self.P
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        R = self.R
+        H = self.H
+        P = self.P
+        x = self.x
+
+        # error (residual) between measurement and prediction
+        y = z - dot(H, x)
+
+        # common subexpression for speed
+        PHT = dot(P, H.T)
+
+        # project system uncertainty into measurement space
+        S = dot(H, PHT) + R
+
+        # map system uncertainty into kalman gain
+        K = dot(PHT, self.inv(S))
+
+        # predict new x with residual scaled by the kalman gain
+        x = x + dot(K, y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        I_KH = self._I - dot(K, H)
+        P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+        return x, P
+
+    def residual_of(self, z):
+        """
+        Returns the residual for the given measurement (z). Does not alter
+        the state of the filter.
+        """
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+        return z - dot(self.H, self.x_prior)
+
+    def measurement_of_state(self, x):
+        """
+        Helper function that converts a state into a measurement.
+        Parameters
+        ----------
+        x : np.array
+            kalman state vector
+        Returns
+        -------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        """
+
+        return dot(self.H, x)
+
+    @property
+    def log_likelihood(self):
+        """
+        log-likelihood of the last measurement.
+        """
+        if self._log_likelihood is None:
+            self._log_likelihood = logpdf(x=self.y, cov=self.S)
+        return self._log_likelihood
+
+    @property
+    def likelihood(self):
+        """
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+        """
+        if self._likelihood is None:
+            self._likelihood = exp(self.log_likelihood)
+            if self._likelihood == 0:
+                self._likelihood = sys.float_info.min
+        return self._likelihood
+
+    @property
+    def mahalanobis(self):
+        """"
+        Mahalanobis distance of measurement. E.g. 3 means measurement
+        was 3 standard deviations away from the predicted value.
+        Returns
+        -------
+        mahalanobis : float
+        """
+        if self._mahalanobis is None:
+            self._mahalanobis = sqrt(float(dot(dot(self.y.T, self.SI), self.y)))
+        return self._mahalanobis
+
+    @property
+    def alpha(self):
+        """
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+        """
+        return self._alpha_sq**.5
+
+    def log_likelihood_of(self, z):
+        """
+        log likelihood of the measurement `z`. This should only be called
+        after a call to update(). Calling after predict() will yield an
+        incorrect result."""
+
+        if z is None:
+            return log(sys.float_info.min)
+        return logpdf(z, dot(self.H, self.x), self.S)
+
+    @alpha.setter
+    def alpha(self, value):
+        if not np.isscalar(value) or value < 1:
+            raise ValueError('alpha must be a float greater than 1')
+
+        self._alpha_sq = value**2
+
+    def __repr__(self):
+        return '\n'.join([
+            'KalmanFilter object',
+            pretty_str('dim_x', self.dim_x),
+            pretty_str('dim_z', self.dim_z),
+            pretty_str('dim_u', self.dim_u),
+            pretty_str('x', self.x),
+            pretty_str('P', self.P),
+            pretty_str('x_prior', self.x_prior),
+            pretty_str('P_prior', self.P_prior),
+            pretty_str('x_post', self.x_post),
+            pretty_str('P_post', self.P_post),
+            pretty_str('F', self.F),
+            pretty_str('Q', self.Q),
+            pretty_str('R', self.R),
+            pretty_str('H', self.H),
+            pretty_str('K', self.K),
+            pretty_str('y', self.y),
+            pretty_str('S', self.S),
+            pretty_str('SI', self.SI),
+            pretty_str('M', self.M),
+            pretty_str('B', self.B),
+            pretty_str('z', self.z),
+            pretty_str('log-likelihood', self.log_likelihood),
+            pretty_str('likelihood', self.likelihood),
+            pretty_str('mahalanobis', self.mahalanobis),
+            pretty_str('alpha', self.alpha),
+            pretty_str('inv', self.inv)
+            ])
+
+    def test_matrix_dimensions(self, z=None, H=None, R=None, F=None, Q=None):
+        """
+        Performs a series of asserts to check that the size of everything
+        is what it should be. This can help you debug problems in your design.
+        If you pass in H, R, F, Q those will be used instead of this object's
+        value for those matrices.
+        Testing `z` (the measurement) is problamatic. x is a vector, and can be
+        implemented as either a 1D array or as a nx1 column vector. Thus Hx
+        can be of different shapes. Then, if Hx is a single value, it can
+        be either a 1D array or 2D vector. If either is true, z can reasonably
+        be a scalar (either '3' or np.array('3') are scalars under this
+        definition), a 1D, 1 element array, or a 2D, 1 element array. You are
+        allowed to pass in any combination that works.
+        """
+
+        if H is None:
+            H = self.H
+        if R is None:
+            R = self.R
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        x = self.x
+        P = self.P
+
+        assert x.ndim == 1 or x.ndim == 2, \
+                "x must have one or two dimensions, but has {}".format(x.ndim)
+
+        if x.ndim == 1:
+            assert x.shape[0] == self.dim_x, \
+                   "Shape of x must be ({},{}), but is {}".format(
+                       self.dim_x, 1, x.shape)
+        else:
+            assert x.shape == (self.dim_x, 1), \
+                   "Shape of x must be ({},{}), but is {}".format(
+                       self.dim_x, 1, x.shape)
+
+        assert P.shape == (self.dim_x, self.dim_x), \
+               "Shape of P must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, P.shape)
+
+        assert Q.shape == (self.dim_x, self.dim_x), \
+               "Shape of Q must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, P.shape)
+
+        assert F.shape == (self.dim_x, self.dim_x), \
+               "Shape of F must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, F.shape)
+
+        assert np.ndim(H) == 2, \
+               "Shape of H must be (dim_z, {}), but is {}".format(
+                   P.shape[0], shape(H))
+
+        assert H.shape[1] == P.shape[0], \
+               "Shape of H must be (dim_z, {}), but is {}".format(
+                   P.shape[0], H.shape)
+
+        # shape of R must be the same as HPH'
+        hph_shape = (H.shape[0], H.shape[0])
+        r_shape = shape(R)
+
+        if H.shape[0] == 1:
+            # r can be scalar, 1D, or 2D in this case
+            assert r_shape in [(), (1,), (1, 1)], \
+            "R must be scalar or one element array, but is shaped {}".format(
+                r_shape)
+        else:
+            assert r_shape == hph_shape, \
+            "shape of R should be {} but it is {}".format(hph_shape, r_shape)
+
+
+        if z is not None:
+            z_shape = shape(z)
+        else:
+            z_shape = (self.dim_z, 1)
+
+        # H@x must have shape of z
+        Hx = dot(H, x)
+
+        if z_shape == (): # scalar or np.array(scalar)
+            assert Hx.ndim == 1 or shape(Hx) == (1, 1), \
+            "shape of z should be {}, not {} for the given H".format(
+                shape(Hx), z_shape)
+
+        elif shape(Hx) == (1,):
+            assert z_shape[0] == 1, 'Shape of z must be {} for the given H'.format(shape(Hx))
+
+        else:
+            assert (z_shape == shape(Hx) or
+                    (len(z_shape) == 1 and shape(Hx) == (z_shape[0], 1))), \
+                    "shape of z should be {}, not {} for the given H".format(
+                        shape(Hx), z_shape)
+
+        if np.ndim(Hx) > 1 and shape(Hx) != (1, 1):
+            assert shape(Hx) == z_shape, \
+               'shape of z should be {} for the given H, but it is {}'.format(
+                   shape(Hx), z_shape)
+
+
+def update(x, P, z, R, H=None, return_all=False):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    update(1, 2, 1, 1, 1)  # univariate
+    update(x, P, 1
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    P : numpy.array(dim_x, dim_x), or float
+        Covariance matrix
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    R : numpy.array(dim_z, dim_z), or float
+        Measurement noise matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    return_all : bool, default False
+        If true, y, K, S, and log_likelihood are returned, otherwise
+        only x and P are returned.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    P : numpy.array
+        Posterior covariance matrix
+    y : numpy.array or scalar
+        Residua. Difference between measurement and state in measurement space
+    K : numpy.array
+        Kalman gain
+    S : numpy.array
+        System uncertainty in measurement space
+    log_likelihood : float
+        log likelihood of the measurement
+    """
+
+    #pylint: disable=bare-except
+
+    if z is None:
+        if return_all:
+            return x, P, None, None, None, None
+        return x, P
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # project system uncertainty into measurement space
+    S = dot(dot(H, P), H.T) + R
+
+
+    # map system uncertainty into kalman gain
+    try:
+        K = dot(dot(P, H.T), linalg.inv(S))
+    except:
+        # can't invert a 1D array, annoyingly
+        K = dot(dot(P, H.T), 1./S)
+
+
+    # predict new x with residual scaled by the kalman gain
+    x = x + dot(K, y)
+
+    # P = (I-KH)P(I-KH)' + KRK'
+    KH = dot(K, H)
+
+    try:
+        I_KH = np.eye(KH.shape[0]) - KH
+    except:
+        I_KH = np.array([1 - KH])
+    P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+
+    if return_all:
+        # compute log likelihood
+        log_likelihood = logpdf(z, dot(H, x), S)
+        return x, P, y, K, S, log_likelihood
+    return x, P
+
+
+def update_steadystate(x, z, K, H=None):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    K : numpy.array, or float
+        Kalman gain matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    Examples
+    --------
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    >>> update_steadystate(1, 2, 1)  # univariate
+    >>> update_steadystate(x, P, z, H)
+    """
+
+
+    if z is None:
+        return x
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # estimate new x with residual scaled by the kalman gain
+    return x + dot(K, y)
+
+
+def predict(x, P, F=1, Q=0, u=0, B=1, alpha=1.):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    Q : numpy.array, Optional
+        Process noise matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    alpha : float, Optional, default=1.0
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    P : numpy.array
+        Prior covariance matrix
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+    P = (alpha * alpha) * dot(dot(F, P), F.T) + Q
+
+    return x, P
+
+
+def predict_steadystate(x, F=1, u=0, B=1):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations. This steady state form only computes x, assuming that the
+    covariance is constant.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+
+    return x
+
+
+
+def batch_filter(x, P, zs, Fs, Qs, Hs, Rs, Bs=None, us=None,
+                 update_first=False, saver=None):
+    """
+    Batch processes a sequences of measurements.
+    Parameters
+    ----------
+    zs : list-like
+        list of measurements at each time step. Missing measurements must be
+        represented by None.
+    Fs : list-like
+        list of values to use for the state transition matrix matrix.
+    Qs : list-like
+        list of values to use for the process error
+        covariance.
+    Hs : list-like
+        list of values to use for the measurement matrix.
+    Rs : list-like
+        list of values to use for the measurement error
+        covariance.
+    Bs : list-like, optional
+        list of values to use for the control transition matrix;
+        a value of None in any position will cause the filter
+        to use `self.B` for that time step.
+    us : list-like, optional
+        list of values to use for the control input vector;
+        a value of None in any position will cause the filter to use
+        0 for that time step.
+    update_first : bool, optional
+        controls whether the order of operations is update followed by
+        predict, or predict followed by update. Default is predict->update.
+        saver : filterpy.common.Saver, optional
+            filterpy.common.Saver object. If provided, saver.save() will be
+            called after every epoch
+    Returns
+    -------
+    means : np.array((n,dim_x,1))
+        array of the state for each time step after the update. Each entry
+        is an np.array. In other words `means[k,:]` is the state at step
+        `k`.
+    covariance : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the update.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    means_predictions : np.array((n,dim_x,1))
+        array of the state for each time step after the predictions. Each
+        entry is an np.array. In other words `means[k,:]` is the state at
+        step `k`.
+    covariance_predictions : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the prediction.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        Fs = [kf.F for t in range (40)]
+        Hs = [kf.H for t in range (40)]
+        (mu, cov, _, _) = kf.batch_filter(zs, Rs=R_list, Fs=Fs, Hs=Hs, Qs=None,
+                                          Bs=None, us=None, update_first=False)
+        (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs, Qs=None)
+    """
+
+    n = np.size(zs, 0)
+    dim_x = x.shape[0]
+
+    # mean estimates from Kalman Filter
+    if x.ndim == 1:
+        means = zeros((n, dim_x))
+        means_p = zeros((n, dim_x))
+    else:
+        means = zeros((n, dim_x, 1))
+        means_p = zeros((n, dim_x, 1))
+
+    # state covariances from Kalman Filter
+    covariances = zeros((n, dim_x, dim_x))
+    covariances_p = zeros((n, dim_x, dim_x))
+
+    if us is None:
+        us = [0.] * n
+        Bs = [0.] * n
+
+    if update_first:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+            if saver is not None:
+                saver.save()
+    else:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+            if saver is not None:
+                saver.save()
+
+    return (means, covariances, means_p, covariances_p)
+
+
+
+def rts_smoother(Xs, Ps, Fs, Qs):
+    """
+    Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+    means and covariances computed by a Kalman filter. The usual input
+    would come from the output of `KalmanFilter.batch_filter()`.
+    Parameters
+    ----------
+    Xs : numpy.array
+       array of the means (state variable x) of the output of a Kalman
+       filter.
+    Ps : numpy.array
+        array of the covariances of the output of a kalman filter.
+    Fs : list-like collection of numpy.array
+        State transition matrix of the Kalman filter at each time step.
+    Qs : list-like collection of numpy.array, optional
+        Process noise of the Kalman filter at each time step.
+    Returns
+    -------
+    x : numpy.ndarray
+       smoothed means
+    P : numpy.ndarray
+       smoothed state covariances
+    K : numpy.ndarray
+        smoother gain at each step
+    pP : numpy.ndarray
+       predicted state covariances
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        (mu, cov, _, _) = kalman.batch_filter(zs)
+        (x, P, K, pP) = rts_smoother(mu, cov, kf.F, kf.Q)
+    """
+
+    if len(Xs) != len(Ps):
+        raise ValueError('length of Xs and Ps must be the same')
+
+    n = Xs.shape[0]
+    dim_x = Xs.shape[1]
+
+    # smoother gain
+    K = zeros((n, dim_x, dim_x))
+    x, P, pP = Xs.copy(), Ps.copy(), Ps.copy()
+
+    for k in range(n-2, -1, -1):
+        pP[k] = dot(dot(Fs[k], P[k]), Fs[k].T) + Qs[k]
+
+        #pylint: disable=bad-whitespace
+        K[k]  = dot(dot(P[k], Fs[k].T), linalg.inv(pP[k]))
+        x[k] += dot(K[k], x[k+1] - dot(Fs[k], x[k]))
+        P[k] += dot(dot(K[k], P[k+1] - pP[k]), K[k].T)
+
+    return (x, P, K, pP)
\ No newline at end of file
diff --git a/trackers/hybrid_sort_tracker/kalmanfilter_score_new.py b/trackers/hybrid_sort_tracker/kalmanfilter_score_new.py
new file mode 100644
index 0000000000000000000000000000000000000000..5a6fe8c0cf28b1c7ddd97f09d89e2f9bcf6aa147
--- /dev/null
+++ b/trackers/hybrid_sort_tracker/kalmanfilter_score_new.py
@@ -0,0 +1,1593 @@
+# -*- coding: utf-8 -*-
+# pylint: disable=invalid-name, too-many-arguments, too-many-branches,
+# pylint: disable=too-many-locals, too-many-instance-attributes, too-many-lines
+
+"""
+This module implements the linear Kalman filter in both an object
+oriented and procedural form. The KalmanFilter class implements
+the filter by storing the various matrices in instance variables,
+minimizing the amount of bookkeeping you have to do.
+All Kalman filters operate with a predict->update cycle. The
+predict step, implemented with the method or function predict(),
+uses the state transition matrix F to predict the state in the next
+time period (epoch). The state is stored as a gaussian (x, P), where
+x is the state (column) vector, and P is its covariance. Covariance
+matrix Q specifies the process covariance. In Bayesian terms, this
+prediction is called the *prior*, which you can think of colloquially
+as the estimate prior to incorporating the measurement.
+The update step, implemented with the method or function `update()`,
+incorporates the measurement z with covariance R, into the state
+estimate (x, P). The class stores the system uncertainty in S,
+the innovation (residual between prediction and measurement in
+measurement space) in y, and the Kalman gain in k. The procedural
+form returns these variables to you. In Bayesian terms this computes
+the *posterior* - the estimate after the information from the
+measurement is incorporated.
+Whether you use the OO form or procedural form is up to you. If
+matrices such as H, R, and F are changing each epoch, you'll probably
+opt to use the procedural form. If they are unchanging, the OO
+form is perhaps easier to use since you won't need to keep track
+of these matrices. This is especially useful if you are implementing
+banks of filters or comparing various KF designs for performance;
+a trivial coding bug could lead to using the wrong sets of matrices.
+This module also offers an implementation of the RTS smoother, and
+other helper functions, such as log likelihood computations.
+The Saver class allows you to easily save the state of the
+KalmanFilter class after every update
+This module expects NumPy arrays for all values that expect
+arrays, although in a few cases, particularly method parameters,
+it will accept types that convert to NumPy arrays, such as lists
+of lists. These exceptions are documented in the method or function.
+Examples
+--------
+The following example constructs a constant velocity kinematic
+filter, filters noisy data, and plots the results. It also demonstrates
+using the Saver class to save the state of the filter at each epoch.
+.. code-block:: Python
+    import matplotlib.pyplot as plt
+    import numpy as np
+    from filterpy.kalman import KalmanFilter
+    from filterpy.common import Q_discrete_white_noise, Saver
+    r_std, q_std = 2., 0.003
+    cv = KalmanFilter(dim_x=2, dim_z=1)
+    cv.x = np.array([[0., 1.]]) # position, velocity
+    cv.F = np.array([[1, dt],[ [0, 1]])
+    cv.R = np.array([[r_std^^2]])
+    f.H = np.array([[1., 0.]])
+    f.P = np.diag([.1^^2, .03^^2)
+    f.Q = Q_discrete_white_noise(2, dt, q_std**2)
+    saver = Saver(cv)
+    for z in range(100):
+        cv.predict()
+        cv.update([z + randn() * r_std])
+        saver.save() # save the filter's state
+    saver.to_array()
+    plt.plot(saver.x[:, 0])
+    # plot all of the priors
+    plt.plot(saver.x_prior[:, 0])
+    # plot mahalanobis distance
+    plt.figure()
+    plt.plot(saver.mahalanobis)
+This code implements the same filter using the procedural form
+    x = np.array([[0., 1.]]) # position, velocity
+    F = np.array([[1, dt],[ [0, 1]])
+    R = np.array([[r_std^^2]])
+    H = np.array([[1., 0.]])
+    P = np.diag([.1^^2, .03^^2)
+    Q = Q_discrete_white_noise(2, dt, q_std**2)
+    for z in range(100):
+        x, P = predict(x, P, F=F, Q=Q)
+        x, P = update(x, P, z=[z + randn() * r_std], R=R, H=H)
+        xs.append(x[0, 0])
+    plt.plot(xs)
+For more examples see the test subdirectory, or refer to the
+book cited below. In it I both teach Kalman filtering from basic
+principles, and teach the use of this library in great detail.
+FilterPy library.
+http://github.com/rlabbe/filterpy
+Documentation at:
+https://filterpy.readthedocs.org
+Supporting book at:
+https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+This is licensed under an MIT license. See the readme.MD file
+for more information.
+Copyright 2014-2018 Roger R Labbe Jr.
+"""
+
+from __future__ import absolute_import, division
+
+from copy import deepcopy
+from math import log, exp, sqrt
+import sys
+import numpy as np
+from numpy import dot, zeros, eye, isscalar, shape
+import numpy.linalg as linalg
+from filterpy.stats import logpdf
+from filterpy.common import pretty_str, reshape_z
+
+
+class KalmanFilterNew_score_new(object):
+    """ Implements a Kalman filter. You are responsible for setting the
+    various state variables to reasonable values; the defaults  will
+    not give you a functional filter.
+    For now the best documentation is my free book Kalman and Bayesian
+    Filters in Python [2]_. The test files in this directory also give you a
+    basic idea of use, albeit without much description.
+    In brief, you will first construct this object, specifying the size of
+    the state vector with dim_x and the size of the measurement vector that
+    you will be using with dim_z. These are mostly used to perform size checks
+    when you assign values to the various matrices. For example, if you
+    specified dim_z=2 and then try to assign a 3x3 matrix to R (the
+    measurement noise matrix you will get an assert exception because R
+    should be 2x2. (If for whatever reason you need to alter the size of
+    things midstream just use the underscore version of the matrices to
+    assign directly: your_filter._R = a_3x3_matrix.)
+    After construction the filter will have default matrices created for you,
+    but you must specify the values for each. It’s usually easiest to just
+    overwrite them rather than assign to each element yourself. This will be
+    clearer in the example below. All are of type numpy.array.
+    Examples
+    --------
+    Here is a filter that tracks position and velocity using a sensor that only
+    reads position.
+    First construct the object with the required dimensionality. Here the state
+    (`dim_x`) has 2 coefficients (position and velocity), and the measurement
+    (`dim_z`) has one. In FilterPy `x` is the state, `z` is the measurement.
+    .. code::
+        from filterpy.kalman import KalmanFilter
+        f = KalmanFilter (dim_x=2, dim_z=1)
+    Assign the initial value for the state (position and velocity). You can do this
+    with a two dimensional array like so:
+        .. code::
+            f.x = np.array([[2.],    # position
+                            [0.]])   # velocity
+    or just use a one dimensional array, which I prefer doing.
+    .. code::
+        f.x = np.array([2., 0.])
+    Define the state transition matrix:
+        .. code::
+            f.F = np.array([[1.,1.],
+                            [0.,1.]])
+    Define the measurement function. Here we need to convert a position-velocity
+    vector into just a position vector, so we use:
+        .. code::
+        f.H = np.array([[1., 0.]])
+    Define the state's covariance matrix P. 
+    .. code::
+        f.P = np.array([[1000.,    0.],
+                        [   0., 1000.] ])
+    Now assign the measurement noise. Here the dimension is 1x1, so I can
+    use a scalar
+    .. code::
+        f.R = 5
+    I could have done this instead:
+    .. code::
+        f.R = np.array([[5.]])
+    Note that this must be a 2 dimensional array.
+    Finally, I will assign the process noise. Here I will take advantage of
+    another FilterPy library function:
+    .. code::
+        from filterpy.common import Q_discrete_white_noise
+        f.Q = Q_discrete_white_noise(dim=2, dt=0.1, var=0.13)
+    Now just perform the standard predict/update loop:
+    .. code::
+        while some_condition_is_true:
+            z = get_sensor_reading()
+            f.predict()
+            f.update(z)
+            do_something_with_estimate (f.x)
+    **Procedural Form**
+    This module also contains stand alone functions to perform Kalman filtering.
+    Use these if you are not a fan of objects.
+    **Example**
+    .. code::
+        while True:
+            z, R = read_sensor()
+            x, P = predict(x, P, F, Q)
+            x, P = update(x, P, z, R, H)
+    See my book Kalman and Bayesian Filters in Python [2]_.
+    You will have to set the following attributes after constructing this
+    object for the filter to perform properly. Please note that there are
+    various checks in place to ensure that you have made everything the
+    'correct' size. However, it is possible to provide incorrectly sized
+    arrays such that the linear algebra can not perform an operation.
+    It can also fail silently - you can end up with matrices of a size that
+    allows the linear algebra to work, but are the wrong shape for the problem
+    you are trying to solve.
+    Parameters
+    ----------
+    dim_x : int
+        Number of state variables for the Kalman filter. For example, if
+        you are tracking the position and velocity of an object in two
+        dimensions, dim_x would be 4.
+        This is used to set the default size of P, Q, and u
+    dim_z : int
+        Number of of measurement inputs. For example, if the sensor
+        provides you with position in (x,y), dim_z would be 2.
+    dim_u : int (optional)
+        size of the control input, if it is being used.
+        Default value of 0 indicates it is not used.
+    compute_log_likelihood : bool (default = True)
+        Computes log likelihood by default, but this can be a slow
+        computation, so if you never use it you can turn this computation
+        off.
+    Attributes
+    ----------
+    x : numpy.array(dim_x, 1)
+        Current state estimate. Any call to update() or predict() updates
+        this variable.
+    P : numpy.array(dim_x, dim_x)
+        Current state covariance matrix. Any call to update() or predict()
+        updates this variable.
+    x_prior : numpy.array(dim_x, 1)
+        Prior (predicted) state estimate. The *_prior and *_post attributes
+        are for convenience; they store the  prior and posterior of the
+        current epoch. Read Only.
+    P_prior : numpy.array(dim_x, dim_x)
+        Prior (predicted) state covariance matrix. Read Only.
+    x_post : numpy.array(dim_x, 1)
+        Posterior (updated) state estimate. Read Only.
+    P_post : numpy.array(dim_x, dim_x)
+        Posterior (updated) state covariance matrix. Read Only.
+    z : numpy.array
+        Last measurement used in update(). Read only.
+    R : numpy.array(dim_z, dim_z)
+        Measurement noise covariance matrix. Also known as the
+        observation covariance.
+    Q : numpy.array(dim_x, dim_x)
+        Process noise covariance matrix. Also known as the transition
+        covariance.
+    F : numpy.array()
+        State Transition matrix. Also known as `A` in some formulation.
+    H : numpy.array(dim_z, dim_x)
+        Measurement function. Also known as the observation matrix, or as `C`.
+    y : numpy.array
+        Residual of the update step. Read only.
+    K : numpy.array(dim_x, dim_z)
+        Kalman gain of the update step. Read only.
+    S :  numpy.array
+        System uncertainty (P projected to measurement space). Read only.
+    SI :  numpy.array
+        Inverse system uncertainty. Read only.
+    log_likelihood : float
+        log-likelihood of the last measurement. Read only.
+    likelihood : float
+        likelihood of last measurement. Read only.
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+    mahalanobis : float
+        mahalanobis distance of the innovation. Read only.
+    inv : function, default numpy.linalg.inv
+        If you prefer another inverse function, such as the Moore-Penrose
+        pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        This is only used to invert self.S. If you know it is diagonal, you
+        might choose to set it to filterpy.common.inv_diagonal, which is
+        several times faster than numpy.linalg.inv for diagonal matrices.
+    alpha : float
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+    References
+    ----------
+    .. [1] Dan Simon. "Optimal State Estimation." John Wiley & Sons.
+       p. 208-212. (2006)
+    .. [2] Roger Labbe. "Kalman and Bayesian Filters in Python"
+       https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+    """
+
+    def __init__(self, dim_x, dim_z, dim_u=0, args=None):
+        if dim_x < 1:
+            raise ValueError('dim_x must be 1 or greater')
+        if dim_z < 1:
+            raise ValueError('dim_z must be 1 or greater')
+        if dim_u < 0:
+            raise ValueError('dim_u must be 0 or greater')
+
+        self.dim_x = dim_x
+        self.dim_z = dim_z
+        self.dim_u = dim_u
+
+        self.x = zeros((dim_x, 1))        # state
+        self.P = eye(dim_x)               # uncertainty covariance
+        self.Q = eye(dim_x)               # process uncertainty
+        self.B = None                     # control transition matrix
+        self.F = eye(dim_x)               # state transition matrix
+        self.H = zeros((dim_z, dim_x))    # measurement function
+        self.R = eye(dim_z)               # measurement uncertainty
+        self._alpha_sq = 1.               # fading memory control
+        self.M = np.zeros((dim_x, dim_z)) # process-measurement cross correlation
+        self.z = np.array([[None]*self.dim_z]).T
+
+        # gain and residual are computed during the innovation step. We
+        # save them so that in case you want to inspect them for various
+        # purposes
+        self.K = np.zeros((dim_x, dim_z)) # kalman gain
+        self.y = zeros((dim_z, 1))
+        self.S = np.zeros((dim_z, dim_z)) # system uncertainty
+        self.SI = np.zeros((dim_z, dim_z)) # inverse system uncertainty
+
+        # identity matrix. Do not alter this.
+        self._I = np.eye(dim_x)
+
+        # these will always be a copy of x,P after predict() is called
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+        # these will always be a copy of x,P after update() is called
+        self.x_post = self.x.copy()             
+        self.P_post = self.P.copy()
+
+        # Only computed only if requested via property
+        self._log_likelihood = log(sys.float_info.min)
+        self._likelihood = sys.float_info.min
+        self._mahalanobis = None
+
+        # keep all observations 
+        self.history_obs = []
+
+        self.inv = np.linalg.inv
+
+        self.attr_saved = None
+        self.observed = False
+        self.args = args
+
+
+    def predict(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            self.x = dot(F, self.x) + dot(B, u)
+        else:
+            self.x = dot(F, self.x)
+
+        # P = FPF' + Q
+        self.P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+
+
+    def freeze(self):
+        """
+            Save the parameters before non-observation forward
+        """
+        self.attr_saved = deepcopy(self.__dict__)
+
+
+    def unfreeze(self):
+        if self.attr_saved is not None:
+            new_history = deepcopy(self.history_obs)
+            self.__dict__ = self.attr_saved
+            # self.history_obs = new_history 
+            self.history_obs = self.history_obs[:-1]
+            occur = [int(d is None) for d in new_history]
+            indices = np.where(np.array(occur)==0)[0]
+            index1 = indices[-2]
+            index2 = indices[-1]
+            box1 = new_history[index1]
+            x1, y1, s1, c1, r1 = box1
+            w1 = np.sqrt(s1 * r1)
+            h1 = np.sqrt(s1 / r1)
+            box2 = new_history[index2]
+            x2, y2, s2, c2, r2 = box2
+            w2 = np.sqrt(s2 * r2)
+            h2 = np.sqrt(s2 / r2)
+            time_gap = index2 - index1
+            dx = (x2-x1)/time_gap
+            dy = (y2-y1)/time_gap 
+            dw = (w2-w1)/time_gap 
+            dh = (h2-h1)/time_gap
+            dc = (c2 - c1) / time_gap
+            for i in range(index2 - index1):
+                """
+                    The default virtual trajectory generation is by linear
+                    motion (constant speed hypothesis), you could modify this 
+                    part to implement your own. 
+                """
+                x = x1 + (i+1) * dx 
+                y = y1 + (i+1) * dy 
+                w = w1 + (i+1) * dw 
+                h = h1 + (i+1) * dh
+                s = w * h 
+                r = w / float(h)
+                c = c1 + (i+1) * dc
+                new_box = np.array([x, y, s, c, r]).reshape((5, 1))
+                """
+                    I still use predict-update loop here to refresh the parameters,
+                    but this can be faster by directly modifying the internal parameters
+                    as suggested in the paper. I keep this naive but slow way for 
+                    easy read and understanding
+                """
+
+                if not i == (index2-index1-1):
+                    self.update(new_box)
+                    self.predict()
+                else:
+                    self.update(new_box)
+
+
+    def update(self, z, R=None, H=None):
+        """
+        Add a new measurement (z) to the Kalman filter.
+        If z is None, nothing is computed. However, x_post and P_post are
+        updated with the prior (x_prior, P_prior), and self.z is set to None.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+            If you pass in a value of H, z must be a column vector the
+            of the correct size.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array, or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise self.H will be used.
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        # append the observation
+        self.history_obs.append(z)
+        
+        if z is None:
+            if self.observed:
+                """
+                    Got no observation so freeze the current parameters for future
+                    potential online smoothing.
+                """
+                self.freeze()
+            self.observed = False 
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+        
+        # self.observed = True
+        if not self.observed:
+            """
+                Get observation, use online smoothing to re-update parameters
+            """
+            self.unfreeze()
+        self.observed = True
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        # if self.args.use_nsa_kalman:
+        #     if confidence > 0.6:
+        #         R = [(1 - confidence) * self.args.nsa_kalman_interval * x for x in R]
+        #     else:
+        #         R = [self.args.nsa_kalman_interval_sec * x for x in R]
+
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # S = HPH' + R
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + R
+        self.SI = self.inv(self.S)
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        # This is more numerically stable
+        # and works for non-optimal K vs the equation
+        # P = (I-KH)P usually seen in the literature.
+
+        I_KH = self._I - dot(self.K, H)
+        self.P = dot(dot(I_KH, self.P), I_KH.T) + dot(dot(self.K, R), self.K.T)
+
+        # save measurement and posterior state
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def predict_steadystate(self, u=0, B=None):
+        """
+        Predict state (prior) using the Kalman filter state propagation
+        equations. Only x is updated, P is left unchanged. See
+        update_steadstate() for a longer explanation of when to use this
+        method.
+        Parameters
+        ----------
+        u : np.array
+            Optional control vector. If non-zero, it is multiplied by B
+            to create the control input into the system.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        """
+
+        if B is None:
+            B = self.B
+
+        # x = Fx + Bu
+        if B is not None:
+            self.x = dot(self.F, self.x) + dot(B, u)
+        else:
+            self.x = dot(self.F, self.x)
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+    def update_steadystate(self, z):
+        """
+        Add a new measurement (z) to the Kalman filter without recomputing
+        the Kalman gain K, the state covariance P, or the system
+        uncertainty S.
+        You can use this for LTI systems since the Kalman gain and covariance
+        converge to a fixed value. Precompute these and assign them explicitly,
+        or run the Kalman filter using the normal predict()/update(0 cycle
+        until they converge.
+        The main advantage of this call is speed. We do significantly less
+        computation, notably avoiding a costly matrix inversion.
+        Use in conjunction with predict_steadystate(), otherwise P will grow
+        without bound.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Examples
+        --------
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> # let filter converge on representative data, then save k and P
+        >>> for i in range(100):
+        >>>     cv.predict()
+        >>>     cv.update([i, i, i])
+        >>> saved_k = np.copy(cv.K)
+        >>> saved_P = np.copy(cv.P)
+        later on:
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> cv.K = np.copy(saved_K)
+        >>> cv.P = np.copy(saved_P)
+        >>> for i in range(100):
+        >>>     cv.predict_steadystate()
+        >>>     cv.update_steadystate([i, i, i])
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(self.H, self.x)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+    def update_correlated(self, z, R=None, H=None):
+        """ Add a new measurement (z) to the Kalman filter assuming that
+        process noise and measurement noise are correlated as defined in
+        the `self.M` matrix.
+        A partial derivation can be found in [1]
+        If z is None, nothing is changed.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array,  or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise  self.H will be used.
+        References
+        ----------
+        .. [1] Bulut, Y. (2011). Applied Kalman filter theory (Doctoral dissertation, Northeastern University).
+               http://people.duke.edu/~hpgavin/SystemID/References/Balut-KalmanFilter-PhD-NEU-2011.pdf
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        # rename for readability and a tiny extra bit of speed
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # handle special case: if z is in form [[z]] but x is not a column
+        # vector dimensions will not match
+        if self.x.ndim == 1 and shape(z) == (1, 1):
+            z = z[0]
+
+        if shape(z) == (): # is it scalar, e.g. z=3 or z=np.array(3)
+            z = np.asarray([z])
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + dot(H, self.M) + dot(self.M.T, H.T) + R
+        self.SI = self.inv(self.S)
+
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT + self.M, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+        self.P = self.P - dot(self.K, dot(H, self.P) + self.M.T)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def batch_filter(self, zs, Fs=None, Qs=None, Hs=None,
+                     Rs=None, Bs=None, us=None, update_first=False,
+                     saver=None):
+        """ Batch processes a sequences of measurements.
+        Parameters
+        ----------
+        zs : list-like
+            list of measurements at each time step `self.dt`. Missing
+            measurements must be represented by `None`.
+        Fs : None, list-like, default=None
+            optional value or list of values to use for the state transition
+            matrix F.
+            If Fs is None then self.F is used for all epochs.
+            Otherwise it must contain a list-like list of F's, one for
+            each epoch.  This allows you to have varying F per epoch.
+        Qs : None, np.array or list-like, default=None
+            optional value or list of values to use for the process error
+            covariance Q.
+            If Qs is None then self.Q is used for all epochs.
+            Otherwise it must contain a list-like list of Q's, one for
+            each epoch.  This allows you to have varying Q per epoch.
+        Hs : None, np.array or list-like, default=None
+            optional list of values to use for the measurement matrix H.
+            If Hs is None then self.H is used for all epochs.
+            If Hs contains a single matrix, then it is used as H for all
+            epochs.
+            Otherwise it must contain a list-like list of H's, one for
+            each epoch.  This allows you to have varying H per epoch.
+        Rs : None, np.array or list-like, default=None
+            optional list of values to use for the measurement error
+            covariance R.
+            If Rs is None then self.R is used for all epochs.
+            Otherwise it must contain a list-like list of R's, one for
+            each epoch.  This allows you to have varying R per epoch.
+        Bs : None, np.array or list-like, default=None
+            optional list of values to use for the control transition matrix B.
+            If Bs is None then self.B is used for all epochs.
+            Otherwise it must contain a list-like list of B's, one for
+            each epoch.  This allows you to have varying B per epoch.
+        us : None, np.array or list-like, default=None
+            optional list of values to use for the control input vector;
+            If us is None then None is used for all epochs (equivalent to 0,
+            or no control input).
+            Otherwise it must contain a list-like list of u's, one for
+            each epoch.
+       update_first : bool, optional, default=False
+            controls whether the order of operations is update followed by
+            predict, or predict followed by update. Default is predict->update.
+        saver : filterpy.common.Saver, optional
+            filterpy.common.Saver object. If provided, saver.save() will be
+            called after every epoch
+        Returns
+        -------
+        means : np.array((n,dim_x,1))
+            array of the state for each time step after the update. Each entry
+            is an np.array. In other words `means[k,:]` is the state at step
+            `k`.
+        covariance : np.array((n,dim_x,dim_x))
+            array of the covariances for each time step after the update.
+            In other words `covariance[k,:,:]` is the covariance at step `k`.
+        means_predictions : np.array((n,dim_x,1))
+            array of the state for each time step after the predictions. Each
+            entry is an np.array. In other words `means[k,:]` is the state at
+            step `k`.
+        covariance_predictions : np.array((n,dim_x,dim_x))
+            array of the covariances for each time step after the prediction.
+            In other words `covariance[k,:,:]` is the covariance at step `k`.
+        Examples
+        --------
+        .. code-block:: Python
+            # this example demonstrates tracking a measurement where the time
+            # between measurement varies, as stored in dts. This requires
+            # that F be recomputed for each epoch. The output is then smoothed
+            # with an RTS smoother.
+            zs = [t + random.randn()*4 for t in range (40)]
+            Fs = [np.array([[1., dt], [0, 1]] for dt in dts]
+            (mu, cov, _, _) = kf.batch_filter(zs, Fs=Fs)
+            (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs)
+        """
+
+        #pylint: disable=too-many-statements
+        n = np.size(zs, 0)
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+        if Hs is None:
+            Hs = [self.H] * n
+        if Rs is None:
+            Rs = [self.R] * n
+        if Bs is None:
+            Bs = [self.B] * n
+        if us is None:
+            us = [0] * n
+
+        # mean estimates from Kalman Filter
+        if self.x.ndim == 1:
+            means = zeros((n, self.dim_x))
+            means_p = zeros((n, self.dim_x))
+        else:
+            means = zeros((n, self.dim_x, 1))
+            means_p = zeros((n, self.dim_x, 1))
+
+        # state covariances from Kalman Filter
+        covariances = zeros((n, self.dim_x, self.dim_x))
+        covariances_p = zeros((n, self.dim_x, self.dim_x))
+
+        if update_first:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+        else:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+
+        return (means, covariances, means_p, covariances_p)
+
+    def rts_smoother(self, Xs, Ps, Fs=None, Qs=None, inv=np.linalg.inv):
+        """
+        Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+        means and covariances computed by a Kalman filter. The usual input
+        would come from the output of `KalmanFilter.batch_filter()`.
+        Parameters
+        ----------
+        Xs : numpy.array
+           array of the means (state variable x) of the output of a Kalman
+           filter.
+        Ps : numpy.array
+            array of the covariances of the output of a kalman filter.
+        Fs : list-like collection of numpy.array, optional
+            State transition matrix of the Kalman filter at each time step.
+            Optional, if not provided the filter's self.F will be used
+        Qs : list-like collection of numpy.array, optional
+            Process noise of the Kalman filter at each time step. Optional,
+            if not provided the filter's self.Q will be used
+        inv : function, default numpy.linalg.inv
+            If you prefer another inverse function, such as the Moore-Penrose
+            pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        Returns
+        -------
+        x : numpy.ndarray
+           smoothed means
+        P : numpy.ndarray
+           smoothed state covariances
+        K : numpy.ndarray
+            smoother gain at each step
+        Pp : numpy.ndarray
+           Predicted state covariances
+        Examples
+        --------
+        .. code-block:: Python
+            zs = [t + random.randn()*4 for t in range (40)]
+            (mu, cov, _, _) = kalman.batch_filter(zs)
+            (x, P, K, Pp) = rts_smoother(mu, cov, kf.F, kf.Q)
+        """
+
+        if len(Xs) != len(Ps):
+            raise ValueError('length of Xs and Ps must be the same')
+
+        n = Xs.shape[0]
+        dim_x = Xs.shape[1]
+
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+
+        # smoother gain
+        K = zeros((n, dim_x, dim_x))
+
+        x, P, Pp = Xs.copy(), Ps.copy(), Ps.copy()
+        for k in range(n-2, -1, -1):
+            Pp[k] = dot(dot(Fs[k+1], P[k]), Fs[k+1].T) + Qs[k+1]
+
+            #pylint: disable=bad-whitespace
+            K[k]  = dot(dot(P[k], Fs[k+1].T), inv(Pp[k]))
+            x[k] += dot(K[k], x[k+1] - dot(Fs[k+1], x[k]))
+            P[k] += dot(dot(K[k], P[k+1] - Pp[k]), K[k].T)
+
+        return (x, P, K, Pp)
+
+    def get_prediction(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations and returns it without modifying the object.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the prediction.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            x = dot(F, self.x) + dot(B, u)
+        else:
+            x = dot(F, self.x)
+
+        # P = FPF' + Q
+        P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        return x, P
+
+    def get_update(self, z=None):
+        """
+        Computes the new estimate based on measurement `z` and returns it
+        without altering the state of the filter.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the update.
+       """
+
+        if z is None:
+            return self.x, self.P
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        R = self.R
+        H = self.H
+        P = self.P
+        x = self.x
+
+        # error (residual) between measurement and prediction
+        y = z - dot(H, x)
+
+        # common subexpression for speed
+        PHT = dot(P, H.T)
+
+        # project system uncertainty into measurement space
+        S = dot(H, PHT) + R
+
+        # map system uncertainty into kalman gain
+        K = dot(PHT, self.inv(S))
+
+        # predict new x with residual scaled by the kalman gain
+        x = x + dot(K, y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        I_KH = self._I - dot(K, H)
+        P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+        return x, P
+
+    def residual_of(self, z):
+        """
+        Returns the residual for the given measurement (z). Does not alter
+        the state of the filter.
+        """
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+        return z - dot(self.H, self.x_prior)
+
+    def measurement_of_state(self, x):
+        """
+        Helper function that converts a state into a measurement.
+        Parameters
+        ----------
+        x : np.array
+            kalman state vector
+        Returns
+        -------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        """
+
+        return dot(self.H, x)
+
+    @property
+    def log_likelihood(self):
+        """
+        log-likelihood of the last measurement.
+        """
+        if self._log_likelihood is None:
+            self._log_likelihood = logpdf(x=self.y, cov=self.S)
+        return self._log_likelihood
+
+    @property
+    def likelihood(self):
+        """
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+        """
+        if self._likelihood is None:
+            self._likelihood = exp(self.log_likelihood)
+            if self._likelihood == 0:
+                self._likelihood = sys.float_info.min
+        return self._likelihood
+
+    @property
+    def mahalanobis(self):
+        """"
+        Mahalanobis distance of measurement. E.g. 3 means measurement
+        was 3 standard deviations away from the predicted value.
+        Returns
+        -------
+        mahalanobis : float
+        """
+        if self._mahalanobis is None:
+            self._mahalanobis = sqrt(float(dot(dot(self.y.T, self.SI), self.y)))
+        return self._mahalanobis
+
+    @property
+    def alpha(self):
+        """
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+        """
+        return self._alpha_sq**.5
+
+    def log_likelihood_of(self, z):
+        """
+        log likelihood of the measurement `z`. This should only be called
+        after a call to update(). Calling after predict() will yield an
+        incorrect result."""
+
+        if z is None:
+            return log(sys.float_info.min)
+        return logpdf(z, dot(self.H, self.x), self.S)
+
+    @alpha.setter
+    def alpha(self, value):
+        if not np.isscalar(value) or value < 1:
+            raise ValueError('alpha must be a float greater than 1')
+
+        self._alpha_sq = value**2
+
+    def __repr__(self):
+        return '\n'.join([
+            'KalmanFilter object',
+            pretty_str('dim_x', self.dim_x),
+            pretty_str('dim_z', self.dim_z),
+            pretty_str('dim_u', self.dim_u),
+            pretty_str('x', self.x),
+            pretty_str('P', self.P),
+            pretty_str('x_prior', self.x_prior),
+            pretty_str('P_prior', self.P_prior),
+            pretty_str('x_post', self.x_post),
+            pretty_str('P_post', self.P_post),
+            pretty_str('F', self.F),
+            pretty_str('Q', self.Q),
+            pretty_str('R', self.R),
+            pretty_str('H', self.H),
+            pretty_str('K', self.K),
+            pretty_str('y', self.y),
+            pretty_str('S', self.S),
+            pretty_str('SI', self.SI),
+            pretty_str('M', self.M),
+            pretty_str('B', self.B),
+            pretty_str('z', self.z),
+            pretty_str('log-likelihood', self.log_likelihood),
+            pretty_str('likelihood', self.likelihood),
+            pretty_str('mahalanobis', self.mahalanobis),
+            pretty_str('alpha', self.alpha),
+            pretty_str('inv', self.inv)
+            ])
+
+    def test_matrix_dimensions(self, z=None, H=None, R=None, F=None, Q=None):
+        """
+        Performs a series of asserts to check that the size of everything
+        is what it should be. This can help you debug problems in your design.
+        If you pass in H, R, F, Q those will be used instead of this object's
+        value for those matrices.
+        Testing `z` (the measurement) is problamatic. x is a vector, and can be
+        implemented as either a 1D array or as a nx1 column vector. Thus Hx
+        can be of different shapes. Then, if Hx is a single value, it can
+        be either a 1D array or 2D vector. If either is true, z can reasonably
+        be a scalar (either '3' or np.array('3') are scalars under this
+        definition), a 1D, 1 element array, or a 2D, 1 element array. You are
+        allowed to pass in any combination that works.
+        """
+
+        if H is None:
+            H = self.H
+        if R is None:
+            R = self.R
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        x = self.x
+        P = self.P
+
+        assert x.ndim == 1 or x.ndim == 2, \
+                "x must have one or two dimensions, but has {}".format(x.ndim)
+
+        if x.ndim == 1:
+            assert x.shape[0] == self.dim_x, \
+                   "Shape of x must be ({},{}), but is {}".format(
+                       self.dim_x, 1, x.shape)
+        else:
+            assert x.shape == (self.dim_x, 1), \
+                   "Shape of x must be ({},{}), but is {}".format(
+                       self.dim_x, 1, x.shape)
+
+        assert P.shape == (self.dim_x, self.dim_x), \
+               "Shape of P must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, P.shape)
+
+        assert Q.shape == (self.dim_x, self.dim_x), \
+               "Shape of Q must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, P.shape)
+
+        assert F.shape == (self.dim_x, self.dim_x), \
+               "Shape of F must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, F.shape)
+
+        assert np.ndim(H) == 2, \
+               "Shape of H must be (dim_z, {}), but is {}".format(
+                   P.shape[0], shape(H))
+
+        assert H.shape[1] == P.shape[0], \
+               "Shape of H must be (dim_z, {}), but is {}".format(
+                   P.shape[0], H.shape)
+
+        # shape of R must be the same as HPH'
+        hph_shape = (H.shape[0], H.shape[0])
+        r_shape = shape(R)
+
+        if H.shape[0] == 1:
+            # r can be scalar, 1D, or 2D in this case
+            assert r_shape in [(), (1,), (1, 1)], \
+            "R must be scalar or one element array, but is shaped {}".format(
+                r_shape)
+        else:
+            assert r_shape == hph_shape, \
+            "shape of R should be {} but it is {}".format(hph_shape, r_shape)
+
+
+        if z is not None:
+            z_shape = shape(z)
+        else:
+            z_shape = (self.dim_z, 1)
+
+        # H@x must have shape of z
+        Hx = dot(H, x)
+
+        if z_shape == (): # scalar or np.array(scalar)
+            assert Hx.ndim == 1 or shape(Hx) == (1, 1), \
+            "shape of z should be {}, not {} for the given H".format(
+                shape(Hx), z_shape)
+
+        elif shape(Hx) == (1,):
+            assert z_shape[0] == 1, 'Shape of z must be {} for the given H'.format(shape(Hx))
+
+        else:
+            assert (z_shape == shape(Hx) or
+                    (len(z_shape) == 1 and shape(Hx) == (z_shape[0], 1))), \
+                    "shape of z should be {}, not {} for the given H".format(
+                        shape(Hx), z_shape)
+
+        if np.ndim(Hx) > 1 and shape(Hx) != (1, 1):
+            assert shape(Hx) == z_shape, \
+               'shape of z should be {} for the given H, but it is {}'.format(
+                   shape(Hx), z_shape)
+
+
+def update(x, P, z, R, H=None, return_all=False):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    update(1, 2, 1, 1, 1)  # univariate
+    update(x, P, 1
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    P : numpy.array(dim_x, dim_x), or float
+        Covariance matrix
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    R : numpy.array(dim_z, dim_z), or float
+        Measurement noise matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    return_all : bool, default False
+        If true, y, K, S, and log_likelihood are returned, otherwise
+        only x and P are returned.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    P : numpy.array
+        Posterior covariance matrix
+    y : numpy.array or scalar
+        Residua. Difference between measurement and state in measurement space
+    K : numpy.array
+        Kalman gain
+    S : numpy.array
+        System uncertainty in measurement space
+    log_likelihood : float
+        log likelihood of the measurement
+    """
+
+    #pylint: disable=bare-except
+
+    if z is None:
+        if return_all:
+            return x, P, None, None, None, None
+        return x, P
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # project system uncertainty into measurement space
+    S = dot(dot(H, P), H.T) + R
+
+
+    # map system uncertainty into kalman gain
+    try:
+        K = dot(dot(P, H.T), linalg.inv(S))
+    except:
+        # can't invert a 1D array, annoyingly
+        K = dot(dot(P, H.T), 1./S)
+
+
+    # predict new x with residual scaled by the kalman gain
+    x = x + dot(K, y)
+
+    # P = (I-KH)P(I-KH)' + KRK'
+    KH = dot(K, H)
+
+    try:
+        I_KH = np.eye(KH.shape[0]) - KH
+    except:
+        I_KH = np.array([1 - KH])
+    P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+
+    if return_all:
+        # compute log likelihood
+        log_likelihood = logpdf(z, dot(H, x), S)
+        return x, P, y, K, S, log_likelihood
+    return x, P
+
+
+def update_steadystate(x, z, K, H=None):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    K : numpy.array, or float
+        Kalman gain matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    Examples
+    --------
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    >>> update_steadystate(1, 2, 1)  # univariate
+    >>> update_steadystate(x, P, z, H)
+    """
+
+
+    if z is None:
+        return x
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # estimate new x with residual scaled by the kalman gain
+    return x + dot(K, y)
+
+
+def predict(x, P, F=1, Q=0, u=0, B=1, alpha=1.):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    Q : numpy.array, Optional
+        Process noise matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    alpha : float, Optional, default=1.0
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    P : numpy.array
+        Prior covariance matrix
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+    P = (alpha * alpha) * dot(dot(F, P), F.T) + Q
+
+    return x, P
+
+
+def predict_steadystate(x, F=1, u=0, B=1):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations. This steady state form only computes x, assuming that the
+    covariance is constant.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+
+    return x
+
+
+
+def batch_filter(x, P, zs, Fs, Qs, Hs, Rs, Bs=None, us=None,
+                 update_first=False, saver=None):
+    """
+    Batch processes a sequences of measurements.
+    Parameters
+    ----------
+    zs : list-like
+        list of measurements at each time step. Missing measurements must be
+        represented by None.
+    Fs : list-like
+        list of values to use for the state transition matrix matrix.
+    Qs : list-like
+        list of values to use for the process error
+        covariance.
+    Hs : list-like
+        list of values to use for the measurement matrix.
+    Rs : list-like
+        list of values to use for the measurement error
+        covariance.
+    Bs : list-like, optional
+        list of values to use for the control transition matrix;
+        a value of None in any position will cause the filter
+        to use `self.B` for that time step.
+    us : list-like, optional
+        list of values to use for the control input vector;
+        a value of None in any position will cause the filter to use
+        0 for that time step.
+    update_first : bool, optional
+        controls whether the order of operations is update followed by
+        predict, or predict followed by update. Default is predict->update.
+        saver : filterpy.common.Saver, optional
+            filterpy.common.Saver object. If provided, saver.save() will be
+            called after every epoch
+    Returns
+    -------
+    means : np.array((n,dim_x,1))
+        array of the state for each time step after the update. Each entry
+        is an np.array. In other words `means[k,:]` is the state at step
+        `k`.
+    covariance : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the update.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    means_predictions : np.array((n,dim_x,1))
+        array of the state for each time step after the predictions. Each
+        entry is an np.array. In other words `means[k,:]` is the state at
+        step `k`.
+    covariance_predictions : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the prediction.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        Fs = [kf.F for t in range (40)]
+        Hs = [kf.H for t in range (40)]
+        (mu, cov, _, _) = kf.batch_filter(zs, Rs=R_list, Fs=Fs, Hs=Hs, Qs=None,
+                                          Bs=None, us=None, update_first=False)
+        (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs, Qs=None)
+    """
+
+    n = np.size(zs, 0)
+    dim_x = x.shape[0]
+
+    # mean estimates from Kalman Filter
+    if x.ndim == 1:
+        means = zeros((n, dim_x))
+        means_p = zeros((n, dim_x))
+    else:
+        means = zeros((n, dim_x, 1))
+        means_p = zeros((n, dim_x, 1))
+
+    # state covariances from Kalman Filter
+    covariances = zeros((n, dim_x, dim_x))
+    covariances_p = zeros((n, dim_x, dim_x))
+
+    if us is None:
+        us = [0.] * n
+        Bs = [0.] * n
+
+    if update_first:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+            if saver is not None:
+                saver.save()
+    else:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+            if saver is not None:
+                saver.save()
+
+    return (means, covariances, means_p, covariances_p)
+
+
+
+def rts_smoother(Xs, Ps, Fs, Qs):
+    """
+    Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+    means and covariances computed by a Kalman filter. The usual input
+    would come from the output of `KalmanFilter.batch_filter()`.
+    Parameters
+    ----------
+    Xs : numpy.array
+       array of the means (state variable x) of the output of a Kalman
+       filter.
+    Ps : numpy.array
+        array of the covariances of the output of a kalman filter.
+    Fs : list-like collection of numpy.array
+        State transition matrix of the Kalman filter at each time step.
+    Qs : list-like collection of numpy.array, optional
+        Process noise of the Kalman filter at each time step.
+    Returns
+    -------
+    x : numpy.ndarray
+       smoothed means
+    P : numpy.ndarray
+       smoothed state covariances
+    K : numpy.ndarray
+        smoother gain at each step
+    pP : numpy.ndarray
+       predicted state covariances
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        (mu, cov, _, _) = kalman.batch_filter(zs)
+        (x, P, K, pP) = rts_smoother(mu, cov, kf.F, kf.Q)
+    """
+
+    if len(Xs) != len(Ps):
+        raise ValueError('length of Xs and Ps must be the same')
+
+    n = Xs.shape[0]
+    dim_x = Xs.shape[1]
+
+    # smoother gain
+    K = zeros((n, dim_x, dim_x))
+    x, P, pP = Xs.copy(), Ps.copy(), Ps.copy()
+
+    for k in range(n-2, -1, -1):
+        pP[k] = dot(dot(Fs[k], P[k]), Fs[k].T) + Qs[k]
+
+        #pylint: disable=bad-whitespace
+        K[k]  = dot(dot(P[k], Fs[k].T), linalg.inv(pP[k]))
+        x[k] += dot(K[k], x[k+1] - dot(Fs[k], x[k]))
+        P[k] += dot(dot(K[k], P[k+1] - pP[k]), K[k].T)
+
+    return (x, P, K, pP)
\ No newline at end of file
diff --git a/trackers/hybrid_sort_tracker/new_kalmanfilter.py b/trackers/hybrid_sort_tracker/new_kalmanfilter.py
new file mode 100644
index 0000000000000000000000000000000000000000..d3c3eeb4bb68bd48593837804d6a2dc8de415227
--- /dev/null
+++ b/trackers/hybrid_sort_tracker/new_kalmanfilter.py
@@ -0,0 +1,1583 @@
+# -*- coding: utf-8 -*-
+# pylint: disable=invalid-name, too-many-arguments, too-many-branches,
+# pylint: disable=too-many-locals, too-many-instance-attributes, too-many-lines
+
+"""
+This module implements the linear Kalman filter in both an object
+oriented and procedural form. The KalmanFilter class implements
+the filter by storing the various matrices in instance variables,
+minimizing the amount of bookkeeping you have to do.
+All Kalman filters operate with a predict->update cycle. The
+predict step, implemented with the method or function predict(),
+uses the state transition matrix F to predict the state in the next
+time period (epoch). The state is stored as a gaussian (x, P), where
+x is the state (column) vector, and P is its covariance. Covariance
+matrix Q specifies the process covariance. In Bayesian terms, this
+prediction is called the *prior*, which you can think of colloquially
+as the estimate prior to incorporating the measurement.
+The update step, implemented with the method or function `update()`,
+incorporates the measurement z with covariance R, into the state
+estimate (x, P). The class stores the system uncertainty in S,
+the innovation (residual between prediction and measurement in
+measurement space) in y, and the Kalman gain in k. The procedural
+form returns these variables to you. In Bayesian terms this computes
+the *posterior* - the estimate after the information from the
+measurement is incorporated.
+Whether you use the OO form or procedural form is up to you. If
+matrices such as H, R, and F are changing each epoch, you'll probably
+opt to use the procedural form. If they are unchanging, the OO
+form is perhaps easier to use since you won't need to keep track
+of these matrices. This is especially useful if you are implementing
+banks of filters or comparing various KF designs for performance;
+a trivial coding bug could lead to using the wrong sets of matrices.
+This module also offers an implementation of the RTS smoother, and
+other helper functions, such as log likelihood computations.
+The Saver class allows you to easily save the state of the
+KalmanFilter class after every update
+This module expects NumPy arrays for all values that expect
+arrays, although in a few cases, particularly method parameters,
+it will accept types that convert to NumPy arrays, such as lists
+of lists. These exceptions are documented in the method or function.
+Examples
+--------
+The following example constructs a constant velocity kinematic
+filter, filters noisy data, and plots the results. It also demonstrates
+using the Saver class to save the state of the filter at each epoch.
+.. code-block:: Python
+    import matplotlib.pyplot as plt
+    import numpy as np
+    from filterpy.kalman import KalmanFilter
+    from filterpy.common import Q_discrete_white_noise, Saver
+    r_std, q_std = 2., 0.003
+    cv = KalmanFilter(dim_x=2, dim_z=1)
+    cv.x = np.array([[0., 1.]]) # position, velocity
+    cv.F = np.array([[1, dt],[ [0, 1]])
+    cv.R = np.array([[r_std^^2]])
+    f.H = np.array([[1., 0.]])
+    f.P = np.diag([.1^^2, .03^^2)
+    f.Q = Q_discrete_white_noise(2, dt, q_std**2)
+    saver = Saver(cv)
+    for z in range(100):
+        cv.predict()
+        cv.update([z + randn() * r_std])
+        saver.save() # save the filter's state
+    saver.to_array()
+    plt.plot(saver.x[:, 0])
+    # plot all of the priors
+    plt.plot(saver.x_prior[:, 0])
+    # plot mahalanobis distance
+    plt.figure()
+    plt.plot(saver.mahalanobis)
+This code implements the same filter using the procedural form
+    x = np.array([[0., 1.]]) # position, velocity
+    F = np.array([[1, dt],[ [0, 1]])
+    R = np.array([[r_std^^2]])
+    H = np.array([[1., 0.]])
+    P = np.diag([.1^^2, .03^^2)
+    Q = Q_discrete_white_noise(2, dt, q_std**2)
+    for z in range(100):
+        x, P = predict(x, P, F=F, Q=Q)
+        x, P = update(x, P, z=[z + randn() * r_std], R=R, H=H)
+        xs.append(x[0, 0])
+    plt.plot(xs)
+For more examples see the test subdirectory, or refer to the
+book cited below. In it I both teach Kalman filtering from basic
+principles, and teach the use of this library in great detail.
+FilterPy library.
+http://github.com/rlabbe/filterpy
+Documentation at:
+https://filterpy.readthedocs.org
+Supporting book at:
+https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+This is licensed under an MIT license. See the readme.MD file
+for more information.
+Copyright 2014-2018 Roger R Labbe Jr.
+"""
+
+from __future__ import absolute_import, division
+
+from copy import deepcopy
+from math import log, exp, sqrt
+import sys
+import numpy as np
+from numpy import dot, zeros, eye, isscalar, shape
+import numpy.linalg as linalg
+from filterpy.stats import logpdf
+from filterpy.common import pretty_str, reshape_z
+
+
+class KalmanFilterNew(object):
+    """ Implements a Kalman filter. You are responsible for setting the
+    various state variables to reasonable values; the defaults  will
+    not give you a functional filter.
+    For now the best documentation is my free book Kalman and Bayesian
+    Filters in Python [2]_. The test files in this directory also give you a
+    basic idea of use, albeit without much description.
+    In brief, you will first construct this object, specifying the size of
+    the state vector with dim_x and the size of the measurement vector that
+    you will be using with dim_z. These are mostly used to perform size checks
+    when you assign values to the various matrices. For example, if you
+    specified dim_z=2 and then try to assign a 3x3 matrix to R (the
+    measurement noise matrix you will get an assert exception because R
+    should be 2x2. (If for whatever reason you need to alter the size of
+    things midstream just use the underscore version of the matrices to
+    assign directly: your_filter._R = a_3x3_matrix.)
+    After construction the filter will have default matrices created for you,
+    but you must specify the values for each. It’s usually easiest to just
+    overwrite them rather than assign to each element yourself. This will be
+    clearer in the example below. All are of type numpy.array.
+    Examples
+    --------
+    Here is a filter that tracks position and velocity using a sensor that only
+    reads position.
+    First construct the object with the required dimensionality. Here the state
+    (`dim_x`) has 2 coefficients (position and velocity), and the measurement
+    (`dim_z`) has one. In FilterPy `x` is the state, `z` is the measurement.
+    .. code::
+        from filterpy.kalman import KalmanFilter
+        f = KalmanFilter (dim_x=2, dim_z=1)
+    Assign the initial value for the state (position and velocity). You can do this
+    with a two dimensional array like so:
+        .. code::
+            f.x = np.array([[2.],    # position
+                            [0.]])   # velocity
+    or just use a one dimensional array, which I prefer doing.
+    .. code::
+        f.x = np.array([2., 0.])
+    Define the state transition matrix:
+        .. code::
+            f.F = np.array([[1.,1.],
+                            [0.,1.]])
+    Define the measurement function. Here we need to convert a position-velocity
+    vector into just a position vector, so we use:
+        .. code::
+        f.H = np.array([[1., 0.]])
+    Define the state's covariance matrix P. 
+    .. code::
+        f.P = np.array([[1000.,    0.],
+                        [   0., 1000.] ])
+    Now assign the measurement noise. Here the dimension is 1x1, so I can
+    use a scalar
+    .. code::
+        f.R = 5
+    I could have done this instead:
+    .. code::
+        f.R = np.array([[5.]])
+    Note that this must be a 2 dimensional array.
+    Finally, I will assign the process noise. Here I will take advantage of
+    another FilterPy library function:
+    .. code::
+        from filterpy.common import Q_discrete_white_noise
+        f.Q = Q_discrete_white_noise(dim=2, dt=0.1, var=0.13)
+    Now just perform the standard predict/update loop:
+    .. code::
+        while some_condition_is_true:
+            z = get_sensor_reading()
+            f.predict()
+            f.update(z)
+            do_something_with_estimate (f.x)
+    **Procedural Form**
+    This module also contains stand alone functions to perform Kalman filtering.
+    Use these if you are not a fan of objects.
+    **Example**
+    .. code::
+        while True:
+            z, R = read_sensor()
+            x, P = predict(x, P, F, Q)
+            x, P = update(x, P, z, R, H)
+    See my book Kalman and Bayesian Filters in Python [2]_.
+    You will have to set the following attributes after constructing this
+    object for the filter to perform properly. Please note that there are
+    various checks in place to ensure that you have made everything the
+    'correct' size. However, it is possible to provide incorrectly sized
+    arrays such that the linear algebra can not perform an operation.
+    It can also fail silently - you can end up with matrices of a size that
+    allows the linear algebra to work, but are the wrong shape for the problem
+    you are trying to solve.
+    Parameters
+    ----------
+    dim_x : int
+        Number of state variables for the Kalman filter. For example, if
+        you are tracking the position and velocity of an object in two
+        dimensions, dim_x would be 4.
+        This is used to set the default size of P, Q, and u
+    dim_z : int
+        Number of of measurement inputs. For example, if the sensor
+        provides you with position in (x,y), dim_z would be 2.
+    dim_u : int (optional)
+        size of the control input, if it is being used.
+        Default value of 0 indicates it is not used.
+    compute_log_likelihood : bool (default = True)
+        Computes log likelihood by default, but this can be a slow
+        computation, so if you never use it you can turn this computation
+        off.
+    Attributes
+    ----------
+    x : numpy.array(dim_x, 1)
+        Current state estimate. Any call to update() or predict() updates
+        this variable.
+    P : numpy.array(dim_x, dim_x)
+        Current state covariance matrix. Any call to update() or predict()
+        updates this variable.
+    x_prior : numpy.array(dim_x, 1)
+        Prior (predicted) state estimate. The *_prior and *_post attributes
+        are for convenience; they store the  prior and posterior of the
+        current epoch. Read Only.
+    P_prior : numpy.array(dim_x, dim_x)
+        Prior (predicted) state covariance matrix. Read Only.
+    x_post : numpy.array(dim_x, 1)
+        Posterior (updated) state estimate. Read Only.
+    P_post : numpy.array(dim_x, dim_x)
+        Posterior (updated) state covariance matrix. Read Only.
+    z : numpy.array
+        Last measurement used in update(). Read only.
+    R : numpy.array(dim_z, dim_z)
+        Measurement noise covariance matrix. Also known as the
+        observation covariance.
+    Q : numpy.array(dim_x, dim_x)
+        Process noise covariance matrix. Also known as the transition
+        covariance.
+    F : numpy.array()
+        State Transition matrix. Also known as `A` in some formulation.
+    H : numpy.array(dim_z, dim_x)
+        Measurement function. Also known as the observation matrix, or as `C`.
+    y : numpy.array
+        Residual of the update step. Read only.
+    K : numpy.array(dim_x, dim_z)
+        Kalman gain of the update step. Read only.
+    S :  numpy.array
+        System uncertainty (P projected to measurement space). Read only.
+    SI :  numpy.array
+        Inverse system uncertainty. Read only.
+    log_likelihood : float
+        log-likelihood of the last measurement. Read only.
+    likelihood : float
+        likelihood of last measurement. Read only.
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+    mahalanobis : float
+        mahalanobis distance of the innovation. Read only.
+    inv : function, default numpy.linalg.inv
+        If you prefer another inverse function, such as the Moore-Penrose
+        pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        This is only used to invert self.S. If you know it is diagonal, you
+        might choose to set it to filterpy.common.inv_diagonal, which is
+        several times faster than numpy.linalg.inv for diagonal matrices.
+    alpha : float
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+    References
+    ----------
+    .. [1] Dan Simon. "Optimal State Estimation." John Wiley & Sons.
+       p. 208-212. (2006)
+    .. [2] Roger Labbe. "Kalman and Bayesian Filters in Python"
+       https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+    """
+
+    def __init__(self, dim_x, dim_z, dim_u=0):
+        if dim_x < 1:
+            raise ValueError('dim_x must be 1 or greater')
+        if dim_z < 1:
+            raise ValueError('dim_z must be 1 or greater')
+        if dim_u < 0:
+            raise ValueError('dim_u must be 0 or greater')
+
+        self.dim_x = dim_x
+        self.dim_z = dim_z
+        self.dim_u = dim_u
+
+        self.x = zeros((dim_x, 1))        # state
+        self.P = eye(dim_x)               # uncertainty covariance
+        self.Q = eye(dim_x)               # process uncertainty
+        self.B = None                     # control transition matrix
+        self.F = eye(dim_x)               # state transition matrix
+        self.H = zeros((dim_z, dim_x))    # measurement function
+        self.R = eye(dim_z)               # measurement uncertainty
+        self._alpha_sq = 1.               # fading memory control
+        self.M = np.zeros((dim_x, dim_z)) # process-measurement cross correlation
+        self.z = np.array([[None]*self.dim_z]).T
+
+        # gain and residual are computed during the innovation step. We
+        # save them so that in case you want to inspect them for various
+        # purposes
+        self.K = np.zeros((dim_x, dim_z)) # kalman gain
+        self.y = zeros((dim_z, 1))
+        self.S = np.zeros((dim_z, dim_z)) # system uncertainty
+        self.SI = np.zeros((dim_z, dim_z)) # inverse system uncertainty
+
+        # identity matrix. Do not alter this.
+        self._I = np.eye(dim_x)
+
+        # these will always be a copy of x,P after predict() is called
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+        # these will always be a copy of x,P after update() is called
+        self.x_post = self.x.copy()             
+        self.P_post = self.P.copy()
+
+        # Only computed only if requested via property
+        self._log_likelihood = log(sys.float_info.min)
+        self._likelihood = sys.float_info.min
+        self._mahalanobis = None
+
+        # keep all observations 
+        self.history_obs = []
+
+        self.inv = np.linalg.inv
+
+        self.attr_saved = None
+        self.observed = False 
+
+
+    def predict(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            self.x = dot(F, self.x) + dot(B, u)
+        else:
+            self.x = dot(F, self.x)
+
+        # P = FPF' + Q
+        self.P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+
+
+    def freeze(self):
+        """
+            Save the parameters before non-observation forward
+        """
+        self.attr_saved = deepcopy(self.__dict__)
+
+
+    def unfreeze(self):
+        if self.attr_saved is not None:
+            new_history = deepcopy(self.history_obs)
+            self.__dict__ = self.attr_saved
+            # self.history_obs = new_history 
+            self.history_obs = self.history_obs[:-1]
+            occur = [int(d is None) for d in new_history]
+            indices = np.where(np.array(occur)==0)[0]
+            index1 = indices[-2]
+            index2 = indices[-1]
+            box1 = new_history[index1]
+            x1, y1, s1, r1, c1 = box1
+            w1 = np.sqrt(s1 * r1)
+            h1 = np.sqrt(s1 / r1)
+            box2 = new_history[index2]
+            x2, y2, s2, r2, c2 = box2
+            w2 = np.sqrt(s2 * r2)
+            h2 = np.sqrt(s2 / r2)
+            time_gap = index2 - index1
+            dx = (x2-x1)/time_gap
+            dy = (y2-y1)/time_gap 
+            dw = (w2-w1)/time_gap 
+            dh = (h2-h1)/time_gap
+            dc = (c2 - c1) / time_gap
+            for i in range(index2 - index1):
+                """
+                    The default virtual trajectory generation is by linear
+                    motion (constant speed hypothesis), you could modify this 
+                    part to implement your own. 
+                """
+                x = x1 + (i+1) * dx 
+                y = y1 + (i+1) * dy 
+                w = w1 + (i+1) * dw 
+                h = h1 + (i+1) * dh
+                s = w * h 
+                r = w / float(h)
+                c = c1 + (i+1) * dc
+                new_box = np.array([x, y, s, r, c]).reshape((5, 1))
+                """
+                    I still use predict-update loop here to refresh the parameters,
+                    but this can be faster by directly modifying the internal parameters
+                    as suggested in the paper. I keep this naive but slow way for 
+                    easy read and understanding
+                """
+                self.update(new_box)
+                if not i == (index2-index1-1):
+                    self.predict()
+
+
+    def update(self, z, R=None, H=None):
+        """
+        Add a new measurement (z) to the Kalman filter.
+        If z is None, nothing is computed. However, x_post and P_post are
+        updated with the prior (x_prior, P_prior), and self.z is set to None.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+            If you pass in a value of H, z must be a column vector the
+            of the correct size.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array, or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise self.H will be used.
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        # append the observation
+        self.history_obs.append(z)
+        
+        if z is None:
+            if self.observed:
+                """
+                    Got no observation so freeze the current parameters for future
+                    potential online smoothing.
+                """
+                self.freeze()
+            self.observed = False 
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+        
+        # self.observed = True
+        if not self.observed:
+            """
+                Get observation, use online smoothing to re-update parameters
+            """
+            self.unfreeze()
+        self.observed = True
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # S = HPH' + R
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + R
+        self.SI = self.inv(self.S)
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        # This is more numerically stable
+        # and works for non-optimal K vs the equation
+        # P = (I-KH)P usually seen in the literature.
+
+        I_KH = self._I - dot(self.K, H)
+        self.P = dot(dot(I_KH, self.P), I_KH.T) + dot(dot(self.K, R), self.K.T)
+
+        # save measurement and posterior state
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def predict_steadystate(self, u=0, B=None):
+        """
+        Predict state (prior) using the Kalman filter state propagation
+        equations. Only x is updated, P is left unchanged. See
+        update_steadstate() for a longer explanation of when to use this
+        method.
+        Parameters
+        ----------
+        u : np.array
+            Optional control vector. If non-zero, it is multiplied by B
+            to create the control input into the system.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        """
+
+        if B is None:
+            B = self.B
+
+        # x = Fx + Bu
+        if B is not None:
+            self.x = dot(self.F, self.x) + dot(B, u)
+        else:
+            self.x = dot(self.F, self.x)
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+    def update_steadystate(self, z):
+        """
+        Add a new measurement (z) to the Kalman filter without recomputing
+        the Kalman gain K, the state covariance P, or the system
+        uncertainty S.
+        You can use this for LTI systems since the Kalman gain and covariance
+        converge to a fixed value. Precompute these and assign them explicitly,
+        or run the Kalman filter using the normal predict()/update(0 cycle
+        until they converge.
+        The main advantage of this call is speed. We do significantly less
+        computation, notably avoiding a costly matrix inversion.
+        Use in conjunction with predict_steadystate(), otherwise P will grow
+        without bound.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Examples
+        --------
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> # let filter converge on representative data, then save k and P
+        >>> for i in range(100):
+        >>>     cv.predict()
+        >>>     cv.update([i, i, i])
+        >>> saved_k = np.copy(cv.K)
+        >>> saved_P = np.copy(cv.P)
+        later on:
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> cv.K = np.copy(saved_K)
+        >>> cv.P = np.copy(saved_P)
+        >>> for i in range(100):
+        >>>     cv.predict_steadystate()
+        >>>     cv.update_steadystate([i, i, i])
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(self.H, self.x)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+    def update_correlated(self, z, R=None, H=None):
+        """ Add a new measurement (z) to the Kalman filter assuming that
+        process noise and measurement noise are correlated as defined in
+        the `self.M` matrix.
+        A partial derivation can be found in [1]
+        If z is None, nothing is changed.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array,  or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise  self.H will be used.
+        References
+        ----------
+        .. [1] Bulut, Y. (2011). Applied Kalman filter theory (Doctoral dissertation, Northeastern University).
+               http://people.duke.edu/~hpgavin/SystemID/References/Balut-KalmanFilter-PhD-NEU-2011.pdf
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None]*self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        # rename for readability and a tiny extra bit of speed
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # handle special case: if z is in form [[z]] but x is not a column
+        # vector dimensions will not match
+        if self.x.ndim == 1 and shape(z) == (1, 1):
+            z = z[0]
+
+        if shape(z) == (): # is it scalar, e.g. z=3 or z=np.array(3)
+            z = np.asarray([z])
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + dot(H, self.M) + dot(self.M.T, H.T) + R
+        self.SI = self.inv(self.S)
+
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT + self.M, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+        self.P = self.P - dot(self.K, dot(H, self.P) + self.M.T)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def batch_filter(self, zs, Fs=None, Qs=None, Hs=None,
+                     Rs=None, Bs=None, us=None, update_first=False,
+                     saver=None):
+        """ Batch processes a sequences of measurements.
+        Parameters
+        ----------
+        zs : list-like
+            list of measurements at each time step `self.dt`. Missing
+            measurements must be represented by `None`.
+        Fs : None, list-like, default=None
+            optional value or list of values to use for the state transition
+            matrix F.
+            If Fs is None then self.F is used for all epochs.
+            Otherwise it must contain a list-like list of F's, one for
+            each epoch.  This allows you to have varying F per epoch.
+        Qs : None, np.array or list-like, default=None
+            optional value or list of values to use for the process error
+            covariance Q.
+            If Qs is None then self.Q is used for all epochs.
+            Otherwise it must contain a list-like list of Q's, one for
+            each epoch.  This allows you to have varying Q per epoch.
+        Hs : None, np.array or list-like, default=None
+            optional list of values to use for the measurement matrix H.
+            If Hs is None then self.H is used for all epochs.
+            If Hs contains a single matrix, then it is used as H for all
+            epochs.
+            Otherwise it must contain a list-like list of H's, one for
+            each epoch.  This allows you to have varying H per epoch.
+        Rs : None, np.array or list-like, default=None
+            optional list of values to use for the measurement error
+            covariance R.
+            If Rs is None then self.R is used for all epochs.
+            Otherwise it must contain a list-like list of R's, one for
+            each epoch.  This allows you to have varying R per epoch.
+        Bs : None, np.array or list-like, default=None
+            optional list of values to use for the control transition matrix B.
+            If Bs is None then self.B is used for all epochs.
+            Otherwise it must contain a list-like list of B's, one for
+            each epoch.  This allows you to have varying B per epoch.
+        us : None, np.array or list-like, default=None
+            optional list of values to use for the control input vector;
+            If us is None then None is used for all epochs (equivalent to 0,
+            or no control input).
+            Otherwise it must contain a list-like list of u's, one for
+            each epoch.
+       update_first : bool, optional, default=False
+            controls whether the order of operations is update followed by
+            predict, or predict followed by update. Default is predict->update.
+        saver : filterpy.common.Saver, optional
+            filterpy.common.Saver object. If provided, saver.save() will be
+            called after every epoch
+        Returns
+        -------
+        means : np.array((n,dim_x,1))
+            array of the state for each time step after the update. Each entry
+            is an np.array. In other words `means[k,:]` is the state at step
+            `k`.
+        covariance : np.array((n,dim_x,dim_x))
+            array of the covariances for each time step after the update.
+            In other words `covariance[k,:,:]` is the covariance at step `k`.
+        means_predictions : np.array((n,dim_x,1))
+            array of the state for each time step after the predictions. Each
+            entry is an np.array. In other words `means[k,:]` is the state at
+            step `k`.
+        covariance_predictions : np.array((n,dim_x,dim_x))
+            array of the covariances for each time step after the prediction.
+            In other words `covariance[k,:,:]` is the covariance at step `k`.
+        Examples
+        --------
+        .. code-block:: Python
+            # this example demonstrates tracking a measurement where the time
+            # between measurement varies, as stored in dts. This requires
+            # that F be recomputed for each epoch. The output is then smoothed
+            # with an RTS smoother.
+            zs = [t + random.randn()*4 for t in range (40)]
+            Fs = [np.array([[1., dt], [0, 1]] for dt in dts]
+            (mu, cov, _, _) = kf.batch_filter(zs, Fs=Fs)
+            (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs)
+        """
+
+        #pylint: disable=too-many-statements
+        n = np.size(zs, 0)
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+        if Hs is None:
+            Hs = [self.H] * n
+        if Rs is None:
+            Rs = [self.R] * n
+        if Bs is None:
+            Bs = [self.B] * n
+        if us is None:
+            us = [0] * n
+
+        # mean estimates from Kalman Filter
+        if self.x.ndim == 1:
+            means = zeros((n, self.dim_x))
+            means_p = zeros((n, self.dim_x))
+        else:
+            means = zeros((n, self.dim_x, 1))
+            means_p = zeros((n, self.dim_x, 1))
+
+        # state covariances from Kalman Filter
+        covariances = zeros((n, self.dim_x, self.dim_x))
+        covariances_p = zeros((n, self.dim_x, self.dim_x))
+
+        if update_first:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+        else:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+
+        return (means, covariances, means_p, covariances_p)
+
+    def rts_smoother(self, Xs, Ps, Fs=None, Qs=None, inv=np.linalg.inv):
+        """
+        Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+        means and covariances computed by a Kalman filter. The usual input
+        would come from the output of `KalmanFilter.batch_filter()`.
+        Parameters
+        ----------
+        Xs : numpy.array
+           array of the means (state variable x) of the output of a Kalman
+           filter.
+        Ps : numpy.array
+            array of the covariances of the output of a kalman filter.
+        Fs : list-like collection of numpy.array, optional
+            State transition matrix of the Kalman filter at each time step.
+            Optional, if not provided the filter's self.F will be used
+        Qs : list-like collection of numpy.array, optional
+            Process noise of the Kalman filter at each time step. Optional,
+            if not provided the filter's self.Q will be used
+        inv : function, default numpy.linalg.inv
+            If you prefer another inverse function, such as the Moore-Penrose
+            pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        Returns
+        -------
+        x : numpy.ndarray
+           smoothed means
+        P : numpy.ndarray
+           smoothed state covariances
+        K : numpy.ndarray
+            smoother gain at each step
+        Pp : numpy.ndarray
+           Predicted state covariances
+        Examples
+        --------
+        .. code-block:: Python
+            zs = [t + random.randn()*4 for t in range (40)]
+            (mu, cov, _, _) = kalman.batch_filter(zs)
+            (x, P, K, Pp) = rts_smoother(mu, cov, kf.F, kf.Q)
+        """
+
+        if len(Xs) != len(Ps):
+            raise ValueError('length of Xs and Ps must be the same')
+
+        n = Xs.shape[0]
+        dim_x = Xs.shape[1]
+
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+
+        # smoother gain
+        K = zeros((n, dim_x, dim_x))
+
+        x, P, Pp = Xs.copy(), Ps.copy(), Ps.copy()
+        for k in range(n-2, -1, -1):
+            Pp[k] = dot(dot(Fs[k+1], P[k]), Fs[k+1].T) + Qs[k+1]
+
+            #pylint: disable=bad-whitespace
+            K[k]  = dot(dot(P[k], Fs[k+1].T), inv(Pp[k]))
+            x[k] += dot(K[k], x[k+1] - dot(Fs[k+1], x[k]))
+            P[k] += dot(dot(K[k], P[k+1] - Pp[k]), K[k].T)
+
+        return (x, P, K, Pp)
+
+    def get_prediction(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations and returns it without modifying the object.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the prediction.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            x = dot(F, self.x) + dot(B, u)
+        else:
+            x = dot(F, self.x)
+
+        # P = FPF' + Q
+        P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        return x, P
+
+    def get_update(self, z=None):
+        """
+        Computes the new estimate based on measurement `z` and returns it
+        without altering the state of the filter.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the update.
+       """
+
+        if z is None:
+            return self.x, self.P
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        R = self.R
+        H = self.H
+        P = self.P
+        x = self.x
+
+        # error (residual) between measurement and prediction
+        y = z - dot(H, x)
+
+        # common subexpression for speed
+        PHT = dot(P, H.T)
+
+        # project system uncertainty into measurement space
+        S = dot(H, PHT) + R
+
+        # map system uncertainty into kalman gain
+        K = dot(PHT, self.inv(S))
+
+        # predict new x with residual scaled by the kalman gain
+        x = x + dot(K, y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        I_KH = self._I - dot(K, H)
+        P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+        return x, P
+
+    def residual_of(self, z):
+        """
+        Returns the residual for the given measurement (z). Does not alter
+        the state of the filter.
+        """
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+        return z - dot(self.H, self.x_prior)
+
+    def measurement_of_state(self, x):
+        """
+        Helper function that converts a state into a measurement.
+        Parameters
+        ----------
+        x : np.array
+            kalman state vector
+        Returns
+        -------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        """
+
+        return dot(self.H, x)
+
+    @property
+    def log_likelihood(self):
+        """
+        log-likelihood of the last measurement.
+        """
+        if self._log_likelihood is None:
+            self._log_likelihood = logpdf(x=self.y, cov=self.S)
+        return self._log_likelihood
+
+    @property
+    def likelihood(self):
+        """
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+        """
+        if self._likelihood is None:
+            self._likelihood = exp(self.log_likelihood)
+            if self._likelihood == 0:
+                self._likelihood = sys.float_info.min
+        return self._likelihood
+
+    @property
+    def mahalanobis(self):
+        """"
+        Mahalanobis distance of measurement. E.g. 3 means measurement
+        was 3 standard deviations away from the predicted value.
+        Returns
+        -------
+        mahalanobis : float
+        """
+        if self._mahalanobis is None:
+            self._mahalanobis = sqrt(float(dot(dot(self.y.T, self.SI), self.y)))
+        return self._mahalanobis
+
+    @property
+    def alpha(self):
+        """
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+        """
+        return self._alpha_sq**.5
+
+    def log_likelihood_of(self, z):
+        """
+        log likelihood of the measurement `z`. This should only be called
+        after a call to update(). Calling after predict() will yield an
+        incorrect result."""
+
+        if z is None:
+            return log(sys.float_info.min)
+        return logpdf(z, dot(self.H, self.x), self.S)
+
+    @alpha.setter
+    def alpha(self, value):
+        if not np.isscalar(value) or value < 1:
+            raise ValueError('alpha must be a float greater than 1')
+
+        self._alpha_sq = value**2
+
+    def __repr__(self):
+        return '\n'.join([
+            'KalmanFilter object',
+            pretty_str('dim_x', self.dim_x),
+            pretty_str('dim_z', self.dim_z),
+            pretty_str('dim_u', self.dim_u),
+            pretty_str('x', self.x),
+            pretty_str('P', self.P),
+            pretty_str('x_prior', self.x_prior),
+            pretty_str('P_prior', self.P_prior),
+            pretty_str('x_post', self.x_post),
+            pretty_str('P_post', self.P_post),
+            pretty_str('F', self.F),
+            pretty_str('Q', self.Q),
+            pretty_str('R', self.R),
+            pretty_str('H', self.H),
+            pretty_str('K', self.K),
+            pretty_str('y', self.y),
+            pretty_str('S', self.S),
+            pretty_str('SI', self.SI),
+            pretty_str('M', self.M),
+            pretty_str('B', self.B),
+            pretty_str('z', self.z),
+            pretty_str('log-likelihood', self.log_likelihood),
+            pretty_str('likelihood', self.likelihood),
+            pretty_str('mahalanobis', self.mahalanobis),
+            pretty_str('alpha', self.alpha),
+            pretty_str('inv', self.inv)
+            ])
+
+    def test_matrix_dimensions(self, z=None, H=None, R=None, F=None, Q=None):
+        """
+        Performs a series of asserts to check that the size of everything
+        is what it should be. This can help you debug problems in your design.
+        If you pass in H, R, F, Q those will be used instead of this object's
+        value for those matrices.
+        Testing `z` (the measurement) is problamatic. x is a vector, and can be
+        implemented as either a 1D array or as a nx1 column vector. Thus Hx
+        can be of different shapes. Then, if Hx is a single value, it can
+        be either a 1D array or 2D vector. If either is true, z can reasonably
+        be a scalar (either '3' or np.array('3') are scalars under this
+        definition), a 1D, 1 element array, or a 2D, 1 element array. You are
+        allowed to pass in any combination that works.
+        """
+
+        if H is None:
+            H = self.H
+        if R is None:
+            R = self.R
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        x = self.x
+        P = self.P
+
+        assert x.ndim == 1 or x.ndim == 2, \
+                "x must have one or two dimensions, but has {}".format(x.ndim)
+
+        if x.ndim == 1:
+            assert x.shape[0] == self.dim_x, \
+                   "Shape of x must be ({},{}), but is {}".format(
+                       self.dim_x, 1, x.shape)
+        else:
+            assert x.shape == (self.dim_x, 1), \
+                   "Shape of x must be ({},{}), but is {}".format(
+                       self.dim_x, 1, x.shape)
+
+        assert P.shape == (self.dim_x, self.dim_x), \
+               "Shape of P must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, P.shape)
+
+        assert Q.shape == (self.dim_x, self.dim_x), \
+               "Shape of Q must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, P.shape)
+
+        assert F.shape == (self.dim_x, self.dim_x), \
+               "Shape of F must be ({},{}), but is {}".format(
+                   self.dim_x, self.dim_x, F.shape)
+
+        assert np.ndim(H) == 2, \
+               "Shape of H must be (dim_z, {}), but is {}".format(
+                   P.shape[0], shape(H))
+
+        assert H.shape[1] == P.shape[0], \
+               "Shape of H must be (dim_z, {}), but is {}".format(
+                   P.shape[0], H.shape)
+
+        # shape of R must be the same as HPH'
+        hph_shape = (H.shape[0], H.shape[0])
+        r_shape = shape(R)
+
+        if H.shape[0] == 1:
+            # r can be scalar, 1D, or 2D in this case
+            assert r_shape in [(), (1,), (1, 1)], \
+            "R must be scalar or one element array, but is shaped {}".format(
+                r_shape)
+        else:
+            assert r_shape == hph_shape, \
+            "shape of R should be {} but it is {}".format(hph_shape, r_shape)
+
+
+        if z is not None:
+            z_shape = shape(z)
+        else:
+            z_shape = (self.dim_z, 1)
+
+        # H@x must have shape of z
+        Hx = dot(H, x)
+
+        if z_shape == (): # scalar or np.array(scalar)
+            assert Hx.ndim == 1 or shape(Hx) == (1, 1), \
+            "shape of z should be {}, not {} for the given H".format(
+                shape(Hx), z_shape)
+
+        elif shape(Hx) == (1,):
+            assert z_shape[0] == 1, 'Shape of z must be {} for the given H'.format(shape(Hx))
+
+        else:
+            assert (z_shape == shape(Hx) or
+                    (len(z_shape) == 1 and shape(Hx) == (z_shape[0], 1))), \
+                    "shape of z should be {}, not {} for the given H".format(
+                        shape(Hx), z_shape)
+
+        if np.ndim(Hx) > 1 and shape(Hx) != (1, 1):
+            assert shape(Hx) == z_shape, \
+               'shape of z should be {} for the given H, but it is {}'.format(
+                   shape(Hx), z_shape)
+
+
+def update(x, P, z, R, H=None, return_all=False):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    update(1, 2, 1, 1, 1)  # univariate
+    update(x, P, 1
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    P : numpy.array(dim_x, dim_x), or float
+        Covariance matrix
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    R : numpy.array(dim_z, dim_z), or float
+        Measurement noise matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    return_all : bool, default False
+        If true, y, K, S, and log_likelihood are returned, otherwise
+        only x and P are returned.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    P : numpy.array
+        Posterior covariance matrix
+    y : numpy.array or scalar
+        Residua. Difference between measurement and state in measurement space
+    K : numpy.array
+        Kalman gain
+    S : numpy.array
+        System uncertainty in measurement space
+    log_likelihood : float
+        log likelihood of the measurement
+    """
+
+    #pylint: disable=bare-except
+
+    if z is None:
+        if return_all:
+            return x, P, None, None, None, None
+        return x, P
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # project system uncertainty into measurement space
+    S = dot(dot(H, P), H.T) + R
+
+
+    # map system uncertainty into kalman gain
+    try:
+        K = dot(dot(P, H.T), linalg.inv(S))
+    except:
+        # can't invert a 1D array, annoyingly
+        K = dot(dot(P, H.T), 1./S)
+
+
+    # predict new x with residual scaled by the kalman gain
+    x = x + dot(K, y)
+
+    # P = (I-KH)P(I-KH)' + KRK'
+    KH = dot(K, H)
+
+    try:
+        I_KH = np.eye(KH.shape[0]) - KH
+    except:
+        I_KH = np.array([1 - KH])
+    P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+
+    if return_all:
+        # compute log likelihood
+        log_likelihood = logpdf(z, dot(H, x), S)
+        return x, P, y, K, S, log_likelihood
+    return x, P
+
+
+def update_steadystate(x, z, K, H=None):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    K : numpy.array, or float
+        Kalman gain matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    Examples
+    --------
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    >>> update_steadystate(1, 2, 1)  # univariate
+    >>> update_steadystate(x, P, z, H)
+    """
+
+
+    if z is None:
+        return x
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # estimate new x with residual scaled by the kalman gain
+    return x + dot(K, y)
+
+
+def predict(x, P, F=1, Q=0, u=0, B=1, alpha=1.):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    Q : numpy.array, Optional
+        Process noise matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    alpha : float, Optional, default=1.0
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    P : numpy.array
+        Prior covariance matrix
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+    P = (alpha * alpha) * dot(dot(F, P), F.T) + Q
+
+    return x, P
+
+
+def predict_steadystate(x, F=1, u=0, B=1):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations. This steady state form only computes x, assuming that the
+    covariance is constant.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+
+    return x
+
+
+
+def batch_filter(x, P, zs, Fs, Qs, Hs, Rs, Bs=None, us=None,
+                 update_first=False, saver=None):
+    """
+    Batch processes a sequences of measurements.
+    Parameters
+    ----------
+    zs : list-like
+        list of measurements at each time step. Missing measurements must be
+        represented by None.
+    Fs : list-like
+        list of values to use for the state transition matrix matrix.
+    Qs : list-like
+        list of values to use for the process error
+        covariance.
+    Hs : list-like
+        list of values to use for the measurement matrix.
+    Rs : list-like
+        list of values to use for the measurement error
+        covariance.
+    Bs : list-like, optional
+        list of values to use for the control transition matrix;
+        a value of None in any position will cause the filter
+        to use `self.B` for that time step.
+    us : list-like, optional
+        list of values to use for the control input vector;
+        a value of None in any position will cause the filter to use
+        0 for that time step.
+    update_first : bool, optional
+        controls whether the order of operations is update followed by
+        predict, or predict followed by update. Default is predict->update.
+        saver : filterpy.common.Saver, optional
+            filterpy.common.Saver object. If provided, saver.save() will be
+            called after every epoch
+    Returns
+    -------
+    means : np.array((n,dim_x,1))
+        array of the state for each time step after the update. Each entry
+        is an np.array. In other words `means[k,:]` is the state at step
+        `k`.
+    covariance : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the update.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    means_predictions : np.array((n,dim_x,1))
+        array of the state for each time step after the predictions. Each
+        entry is an np.array. In other words `means[k,:]` is the state at
+        step `k`.
+    covariance_predictions : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the prediction.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        Fs = [kf.F for t in range (40)]
+        Hs = [kf.H for t in range (40)]
+        (mu, cov, _, _) = kf.batch_filter(zs, Rs=R_list, Fs=Fs, Hs=Hs, Qs=None,
+                                          Bs=None, us=None, update_first=False)
+        (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs, Qs=None)
+    """
+
+    n = np.size(zs, 0)
+    dim_x = x.shape[0]
+
+    # mean estimates from Kalman Filter
+    if x.ndim == 1:
+        means = zeros((n, dim_x))
+        means_p = zeros((n, dim_x))
+    else:
+        means = zeros((n, dim_x, 1))
+        means_p = zeros((n, dim_x, 1))
+
+    # state covariances from Kalman Filter
+    covariances = zeros((n, dim_x, dim_x))
+    covariances_p = zeros((n, dim_x, dim_x))
+
+    if us is None:
+        us = [0.] * n
+        Bs = [0.] * n
+
+    if update_first:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+            if saver is not None:
+                saver.save()
+    else:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+            if saver is not None:
+                saver.save()
+
+    return (means, covariances, means_p, covariances_p)
+
+
+
+def rts_smoother(Xs, Ps, Fs, Qs):
+    """
+    Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+    means and covariances computed by a Kalman filter. The usual input
+    would come from the output of `KalmanFilter.batch_filter()`.
+    Parameters
+    ----------
+    Xs : numpy.array
+       array of the means (state variable x) of the output of a Kalman
+       filter.
+    Ps : numpy.array
+        array of the covariances of the output of a kalman filter.
+    Fs : list-like collection of numpy.array
+        State transition matrix of the Kalman filter at each time step.
+    Qs : list-like collection of numpy.array, optional
+        Process noise of the Kalman filter at each time step.
+    Returns
+    -------
+    x : numpy.ndarray
+       smoothed means
+    P : numpy.ndarray
+       smoothed state covariances
+    K : numpy.ndarray
+        smoother gain at each step
+    pP : numpy.ndarray
+       predicted state covariances
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        (mu, cov, _, _) = kalman.batch_filter(zs)
+        (x, P, K, pP) = rts_smoother(mu, cov, kf.F, kf.Q)
+    """
+
+    if len(Xs) != len(Ps):
+        raise ValueError('length of Xs and Ps must be the same')
+
+    n = Xs.shape[0]
+    dim_x = Xs.shape[1]
+
+    # smoother gain
+    K = zeros((n, dim_x, dim_x))
+    x, P, pP = Xs.copy(), Ps.copy(), Ps.copy()
+
+    for k in range(n-2, -1, -1):
+        pP[k] = dot(dot(Fs[k], P[k]), Fs[k].T) + Qs[k]
+
+        #pylint: disable=bad-whitespace
+        K[k]  = dot(dot(P[k], Fs[k].T), linalg.inv(pP[k]))
+        x[k] += dot(K[k], x[k+1] - dot(Fs[k], x[k]))
+        P[k] += dot(dot(K[k], P[k+1] - pP[k]), K[k].T)
+
+    return (x, P, K, pP)
\ No newline at end of file
diff --git a/trackers/integrated_ocsort_embedding/__init__.py b/trackers/integrated_ocsort_embedding/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..173109afc3f8bd0d3f4023e0fd98029e62e8cf23
--- /dev/null
+++ b/trackers/integrated_ocsort_embedding/__init__.py
@@ -0,0 +1,2 @@
+from . import args
+from . import ocsort
diff --git a/trackers/integrated_ocsort_embedding/args.py b/trackers/integrated_ocsort_embedding/args.py
new file mode 100644
index 0000000000000000000000000000000000000000..4bc57ad5280e2c837c01149adf259224686ade8a
--- /dev/null
+++ b/trackers/integrated_ocsort_embedding/args.py
@@ -0,0 +1,110 @@
+import argparse
+
+
+def make_parser():
+    parser = argparse.ArgumentParser("OC-SORT parameters")
+
+    # distributed
+    parser.add_argument("-b", "--batch-size", type=int, default=1, help="batch size")
+    parser.add_argument("-d", "--devices", default=None, type=int, help="device for training")
+
+    parser.add_argument("--local_rank", default=0, type=int, help="local rank for dist training")
+    parser.add_argument("--num_machines", default=1, type=int, help="num of node for training")
+    parser.add_argument("--machine_rank", default=0, type=int, help="node rank for multi-node training")
+
+    parser.add_argument(
+        "-f",
+        "--exp_file",
+        default=None,
+        type=str,
+        help="pls input your expriment description file",
+    )
+    parser.add_argument(
+        "--test",
+        dest="test",
+        default=False,
+        action="store_true",
+        help="Evaluating on test-dev set.",
+    )
+    parser.add_argument(
+        "opts",
+        help="Modify config options using the command-line",
+        default=None,
+        nargs=argparse.REMAINDER,
+    )
+
+    # det args
+    parser.add_argument("-c", "--ckpt", default=None, type=str, help="ckpt for eval")
+    parser.add_argument("--conf", default=0.1, type=float, help="test conf")
+    parser.add_argument("--nms", default=0.7, type=float, help="test nms threshold")
+    parser.add_argument("--tsize", default=[800, 1440], nargs="+", type=int, help="test img size")
+    parser.add_argument("--seed", default=None, type=int, help="eval seed")
+
+    # tracking args
+    parser.add_argument("--track_thresh", type=float, default=0.6, help="detection confidence threshold")
+    parser.add_argument(
+        "--iou_thresh",
+        type=float,
+        default=0.3,
+        help="the iou threshold in Sort for matching",
+    )
+    parser.add_argument("--min_hits", type=int, default=3, help="min hits to create track in SORT")
+    parser.add_argument(
+        "--inertia",
+        type=float,
+        default=0.2,
+        help="the weight of VDC term in cost matrix",
+    )
+    parser.add_argument(
+        "--deltat",
+        type=int,
+        default=3,
+        help="time step difference to estimate direction",
+    )
+    parser.add_argument("--track_buffer", type=int, default=30, help="the frames for keep lost tracks")
+    parser.add_argument(
+        "--match_thresh",
+        type=float,
+        default=0.9,
+        help="matching threshold for tracking",
+    )
+    parser.add_argument(
+        "--gt-type",
+        type=str,
+        default="_val_half",
+        help="suffix to find the gt annotation",
+    )
+    parser.add_argument("--public", action="store_true", help="use public detection")
+    parser.add_argument("--asso", default="iou", help="similarity function: iou/giou/diou/ciou/ctdis")
+
+    # for kitti/bdd100k inference with public detections
+    parser.add_argument(
+        "--raw_results_path",
+        type=str,
+        default="exps/permatrack_kitti_test/",
+        help="path to the raw tracking results from other tracks",
+    )
+    parser.add_argument("--out_path", type=str, help="path to save output results")
+    parser.add_argument(
+        "--hp",
+        action="store_true",
+        help="use head padding to add the missing objects during \
+            initializing the tracks (offline).",
+    )
+
+    # for demo video
+    parser.add_argument("--demo_type", default="image", help="demo type, eg. image, video and webcam")
+    parser.add_argument("--path", default="./videos/demo.mp4", help="path to images or video")
+    parser.add_argument("--camid", type=int, default=0, help="webcam demo camera id")
+    parser.add_argument(
+        "--save_result",
+        action="store_true",
+        help="whether to save the inference result of image/video",
+    )
+    parser.add_argument(
+        "--device",
+        default="gpu",
+        type=str,
+        help="device to run our model, can either be cpu or gpu",
+    )
+    return parser
diff --git a/trackers/integrated_ocsort_embedding/association.py b/trackers/integrated_ocsort_embedding/association.py
new file mode 100644
index 0000000000000000000000000000000000000000..ddbe757004e6ae24d0ad26db49cf802909afc1f2
--- /dev/null
+++ b/trackers/integrated_ocsort_embedding/association.py
@@ -0,0 +1,480 @@
+import numpy as np
+import scipy.spatial as sp
+
+
+def iou_batch(bboxes1, bboxes2):
+    """
+    From SORT: Computes IOU between two bboxes in the form [x1,y1,x2,y2]
+    """
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0.0, xx2 - xx1)
+    h = np.maximum(0.0, yy2 - yy1)
+    wh = w * h
+    o = wh / (
+        (bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1])
+        - wh
+    )
+    return o
+
+
+def giou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0.0, xx2 - xx1)
+    h = np.maximum(0.0, yy2 - yy1)
+    wh = w * h
+    iou = wh / (
+        (bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1])
+        - wh
+    )
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+    wc = xxc2 - xxc1
+    hc = yyc2 - yyc1
+    assert (wc > 0).all() and (hc > 0).all()
+    area_enclose = wc * hc
+    giou = iou - (area_enclose - wh) / area_enclose
+    giou = (giou + 1.0) / 2.0  # resize from (-1,1) to (0,1)
+    return giou
+
+
+def diou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    # calculate the intersection box
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0.0, xx2 - xx1)
+    h = np.maximum(0.0, yy2 - yy1)
+    wh = w * h
+    iou = wh / (
+        (bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1])
+        - wh
+    )
+
+    centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
+    centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
+    centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
+    centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
+
+    inner_diag = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+
+    outer_diag = (xxc2 - xxc1) ** 2 + (yyc2 - yyc1) ** 2
+    diou = iou - inner_diag / outer_diag
+
+    return (diou + 1) / 2.0  # resize from (-1,1) to (0,1)
+
+
+def ciou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    # calculate the intersection box
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0.0, xx2 - xx1)
+    h = np.maximum(0.0, yy2 - yy1)
+    wh = w * h
+    iou = wh / (
+        (bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1])
+        - wh
+    )
+
+    centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
+    centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
+    centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
+    centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
+
+    inner_diag = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+
+    outer_diag = (xxc2 - xxc1) ** 2 + (yyc2 - yyc1) ** 2
+
+    w1 = bboxes1[..., 2] - bboxes1[..., 0]
+    h1 = bboxes1[..., 3] - bboxes1[..., 1]
+    w2 = bboxes2[..., 2] - bboxes2[..., 0]
+    h2 = bboxes2[..., 3] - bboxes2[..., 1]
+
+    # prevent dividing over zero. add one pixel shift
+    h2 = h2 + 1.0
+    h1 = h1 + 1.0
+    arctan = np.arctan(w2 / h2) - np.arctan(w1 / h1)
+    v = (4 / (np.pi**2)) * (arctan**2)
+    S = 1 - iou
+    alpha = v / (S + v)
+    ciou = iou - inner_diag / outer_diag - alpha * v
+
+    return (ciou + 1) / 2.0  # resize from (-1,1) to (0,1)
+
+
+def ct_dist(bboxes1, bboxes2):
+    """
+    Measure the center distance between two sets of bounding boxes,
+    this is a coarse implementation, we don't recommend using it only
+    for association, which can be unstable and sensitive to frame rate
+    and object speed.
+    """
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
+    centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
+    centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
+    centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
+
+    ct_dist2 = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
+
+    ct_dist = np.sqrt(ct_dist2)
+
+    # The linear rescaling is a naive version and needs more study
+    ct_dist = ct_dist / ct_dist.max()
+    return ct_dist.max() - ct_dist  # resize to (0,1)
+
+
+def speed_direction_batch(dets, tracks):
+    tracks = tracks[..., np.newaxis]
+    CX1, CY1 = (dets[:, 0] + dets[:, 2]) / 2.0, (dets[:, 1] + dets[:, 3]) / 2.0
+    CX2, CY2 = (tracks[:, 0] + tracks[:, 2]) / 2.0, (tracks[:, 1] + tracks[:, 3]) / 2.0
+    dx = CX1 - CX2
+    dy = CY1 - CY2
+    norm = np.sqrt(dx**2 + dy**2) + 1e-6
+    dx = dx / norm
+    dy = dy / norm
+    return dy, dx  # size: num_track x num_det
+
+
+def linear_assignment(cost_matrix):
+    try:
+        import lap
+
+        _, x, y = lap.lapjv(cost_matrix, extend_cost=True)
+        return np.array([[y[i], i] for i in x if i >= 0])  #
+    except ImportError:
+        from scipy.optimize import linear_sum_assignment
+
+        x, y = linear_sum_assignment(cost_matrix)
+        return np.array(list(zip(x, y)))
+
+
+def associate_detections_to_trackers(detections, trackers, iou_threshold=0.3):
+    """
+    Assigns detections to tracked object (both represented as bounding boxes)
+    Returns 3 lists of matches, unmatched_detections and unmatched_trackers
+    """
+    if len(trackers) == 0:
+        return (
+            np.empty((0, 2), dtype=int),
+            np.arange(len(detections)),
+            np.empty((0, 5), dtype=int),
+        )
+
+    iou_matrix = iou_batch(detections, trackers)
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(-iou_matrix)
+    else:
+        matched_indices = np.empty(shape=(0, 2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if d not in matched_indices[:, 0]:
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if t not in matched_indices[:, 1]:
+            unmatched_trackers.append(t)
+
+    # filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if iou_matrix[m[0], m[1]] < iou_threshold:
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1, 2))
+    if len(matches) == 0:
+        matches = np.empty((0, 2), dtype=int)
+    else:
+        matches = np.concatenate(matches, axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+
+def compute_aw_new_metric(emb_cost, w_association_emb, max_diff=0.5):
+    w_emb = np.full_like(emb_cost, w_association_emb)
+    w_emb_bonus = np.full_like(emb_cost, 0)
+
+    # Needs two columns at least to make sense to boost
+    if emb_cost.shape[1] >= 2:
+        # Across all rows
+        for idx in range(emb_cost.shape[0]):
+            inds = np.argsort(-emb_cost[idx])
+            # Row weight is difference between top / second top
+            row_weight = min(emb_cost[idx, inds[0]] - emb_cost[idx, inds[1]], max_diff)
+            # Add to row
+            w_emb_bonus[idx] += row_weight / 2
+
+    if emb_cost.shape[0] >= 2:
+        for idj in range(emb_cost.shape[1]):
+            inds = np.argsort(-emb_cost[:, idj])
+            col_weight = min(emb_cost[inds[0], idj] - emb_cost[inds[1], idj], max_diff)
+            w_emb_bonus[:, idj] += col_weight / 2
+
+    return w_emb + w_emb_bonus
+
+
+def split_cosine_dist(dets, trks, affinity_thresh=0.55, pair_diff_thresh=0.6, hard_thresh=True):
+
+    cos_dist = np.zeros((len(dets), len(trks)))
+
+    for i in range(len(dets)):
+        for j in range(len(trks)):
+
+            cos_d = 1 - sp.distance.cdist(dets[i], trks[j], "cosine")  ## shape = 3x3
+            patch_affinity = np.max(cos_d, axis=0)  ## shape = [3,]
+            # exp16 - Using Hard threshold
+            if hard_thresh:
+                if len(np.where(patch_affinity > affinity_thresh)[0]) != len(patch_affinity):
+                    cos_dist[i, j] = 0
+                else:
+                    cos_dist[i, j] = np.max(patch_affinity)
+            else:
+                cos_dist[i, j] = np.max(patch_affinity)  # can experiment with mean too (max works slightly better)
+
+    return cos_dist
+
+
+def associate(
+    detections,
+    trackers,
+    det_embs,
+    trk_embs,
+    iou_threshold,
+    velocities,
+    previous_obs,
+    vdc_weight,
+    w_assoc_emb,
+    aw_off,
+    aw_param,
+    emb_off,
+    grid_off,
+):
+    if len(trackers) == 0:
+        return (
+            np.empty((0, 2), dtype=int),
+            np.arange(len(detections)),
+            np.empty((0, 5), dtype=int),
+        )
+
+    Y, X = speed_direction_batch(detections, previous_obs)
+    inertia_Y, inertia_X = velocities[:, 0], velocities[:, 1]
+    inertia_Y = np.repeat(inertia_Y[:, np.newaxis], Y.shape[1], axis=1)
+    inertia_X = np.repeat(inertia_X[:, np.newaxis], X.shape[1], axis=1)
+    diff_angle_cos = inertia_X * X + inertia_Y * Y
+    diff_angle_cos = np.clip(diff_angle_cos, a_min=-1, a_max=1)
+    diff_angle = np.arccos(diff_angle_cos)
+    diff_angle = (np.pi / 2.0 - np.abs(diff_angle)) / np.pi
+
+    valid_mask = np.ones(previous_obs.shape[0])
+    valid_mask[np.where(previous_obs[:, 4] < 0)] = 0
+
+    iou_matrix = iou_batch(detections, trackers)
+    scores = np.repeat(detections[:, -1][:, np.newaxis], trackers.shape[0], axis=1)
+    # iou_matrix = iou_matrix * scores # a trick sometiems works, we don't encourage this
+    valid_mask = np.repeat(valid_mask[:, np.newaxis], X.shape[1], axis=1)
+
+    angle_diff_cost = (valid_mask * diff_angle) * vdc_weight
+    angle_diff_cost = angle_diff_cost.T
+    angle_diff_cost = angle_diff_cost * scores
+
+    emb_cost = None
+    if not emb_off:
+        if grid_off:
+            emb_cost = None if (trk_embs.shape[0] == 0 or det_embs.shape[0] == 0) else det_embs @ trk_embs.T
+        else:
+            # emb_cost = split_cosine_dist(det_embs, trk_embs)
+            emb_cost = 1 - sp.distance.cdist(det_embs, trk_embs, "cosine")
+            emb_cost[emb_cost > 0.55] = 0  # affinity_thresh
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            if emb_cost is None:
+                emb_cost = 0
+            else:
+                # emb_cost[iou_matrix <= 0.3] = 0
+                pass
+            if not aw_off:
+                w_matrix = compute_aw_new_metric(emb_cost, w_assoc_emb, aw_param)
+                emb_cost *= w_matrix
+            else:
+                emb_cost *= w_assoc_emb
+
+            final_cost = -(iou_matrix + angle_diff_cost + emb_cost)
+            matched_indices = linear_assignment(final_cost)
+    else:
+        matched_indices = np.empty(shape=(0, 2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if d not in matched_indices[:, 0]:
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if t not in matched_indices[:, 1]:
+            unmatched_trackers.append(t)
+
+    # filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if iou_matrix[m[0], m[1]] < iou_threshold:
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1, 2))
+    if len(matches) == 0:
+        matches = np.empty((0, 2), dtype=int)
+    else:
+        matches = np.concatenate(matches, axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+
+def associate_kitti(detections, trackers, det_cates, iou_threshold, velocities, previous_obs, vdc_weight):
+    if len(trackers) == 0:
+        return (
+            np.empty((0, 2), dtype=int),
+            np.arange(len(detections)),
+            np.empty((0, 5), dtype=int),
+        )
+
+    """
+        Cost from the velocity direction consistency
+    """
+    Y, X = speed_direction_batch(detections, previous_obs)
+    inertia_Y, inertia_X = velocities[:, 0], velocities[:, 1]
+    inertia_Y = np.repeat(inertia_Y[:, np.newaxis], Y.shape[1], axis=1)
+    inertia_X = np.repeat(inertia_X[:, np.newaxis], X.shape[1], axis=1)
+    diff_angle_cos = inertia_X * X + inertia_Y * Y
+    diff_angle_cos = np.clip(diff_angle_cos, a_min=-1, a_max=1)
+    diff_angle = np.arccos(diff_angle_cos)
+    diff_angle = (np.pi / 2.0 - np.abs(diff_angle)) / np.pi
+
+    valid_mask = np.ones(previous_obs.shape[0])
+    valid_mask[np.where(previous_obs[:, 4] < 0)] = 0
+    valid_mask = np.repeat(valid_mask[:, np.newaxis], X.shape[1], axis=1)
+
+    scores = np.repeat(detections[:, -1][:, np.newaxis], trackers.shape[0], axis=1)
+    angle_diff_cost = (valid_mask * diff_angle) * vdc_weight
+    angle_diff_cost = angle_diff_cost.T
+    angle_diff_cost = angle_diff_cost * scores
+
+    """
+        Cost from IoU
+    """
+    iou_matrix = iou_batch(detections, trackers)
+
+    """
+        With multiple categories, generate the cost for catgory mismatch
+    """
+    num_dets = detections.shape[0]
+    num_trk = trackers.shape[0]
+    cate_matrix = np.zeros((num_dets, num_trk))
+    for i in range(num_dets):
+        for j in range(num_trk):
+            if det_cates[i] != trackers[j, 4]:
+                cate_matrix[i][j] = -1e6
+
+    cost_matrix = -iou_matrix - angle_diff_cost - cate_matrix
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(cost_matrix)
+    else:
+        matched_indices = np.empty(shape=(0, 2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if d not in matched_indices[:, 0]:
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if t not in matched_indices[:, 1]:
+            unmatched_trackers.append(t)
+
+    # filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if iou_matrix[m[0], m[1]] < iou_threshold:
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1, 2))
+    if len(matches) == 0:
+        matches = np.empty((0, 2), dtype=int)
+    else:
+        matches = np.concatenate(matches, axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
diff --git a/trackers/integrated_ocsort_embedding/cmc.py b/trackers/integrated_ocsort_embedding/cmc.py
new file mode 100644
index 0000000000000000000000000000000000000000..85f63a7581d4317aca44b6956e6eb6935c16dccc
--- /dev/null
+++ b/trackers/integrated_ocsort_embedding/cmc.py
@@ -0,0 +1,177 @@
+import pdb
+import pickle
+import os
+
+import cv2
+import numpy as np
+
+
+class CMCComputer:
+    def __init__(self, minimum_features=10, method="file"):
+        assert method in ["file", "sparse", "sift"]
+
+        os.makedirs("./cache", exist_ok=True)
+        self.cache_path = "./cache/affine_ocsort.pkl"
+        self.cache = {}
+        # if os.path.exists(self.cache_path):
+        #    with open(self.cache_path, "rb") as fp:
+        #        self.cache = pickle.load(fp)
+        self.minimum_features = minimum_features
+        self.prev_img = None
+        self.prev_desc = None
+        self.sparse_flow_param = dict(
+            maxCorners=3000,
+            qualityLevel=0.01,
+            minDistance=1,
+            blockSize=3,
+            useHarrisDetector=False,
+            k=0.04,
+        )
+        self.file_computed = {}
+
+        self.comp_function = None
+        if method == "sparse":
+            self.comp_function = self._affine_sparse_flow
+        elif method == "sift":
+            self.comp_function = self._affine_sift
+        # Same BoT-SORT CMC arrays
+        elif method == "file":
+            self.comp_function = self._affine_file
+            self.file_affines = {}
+            # Maps from tag name to file name
+            self.file_names = {}
+
+            # DanceTrack
+            for f_name in os.listdir("./cache/cmc_files/DanceTrack/"):
+                tag = f_name.replace("GMC-", "").replace(".txt", "").replace("-", "")
+                f_name = os.path.join("./cache/cmc_files/DanceTrack/", f_name)
+                self.file_names[tag] = f_name
+
+            # All the ablation file names
+            for f_name in os.listdir("./cache/cmc_files/MOT17_ablation/"):
+                # The tag that'll be passed into compute_affine based on image name
+                tag = f_name.replace("GMC-", "").replace(".txt", "") + "-FRCNN"
+                f_name = os.path.join("./cache/cmc_files/MOT17_ablation/", f_name)
+                self.file_names[tag] = f_name
+            for f_name in os.listdir("./cache/cmc_files/MOT20_ablation/"):
+                tag = f_name.replace("GMC-", "").replace(".txt", "")
+                f_name = os.path.join("./cache/cmc_files/MOT20_ablation/", f_name)
+                self.file_names[tag] = f_name
+
+            # All the test file names
+            for f_name in os.listdir("./cache/cmc_files/MOTChallenge/"):
+                tag = f_name.replace("GMC-", "").replace(".txt", "")
+                if "MOT17" in tag:
+                    tag = tag + "-FRCNN"
+                # If it's an ablation one (not test) don't overwrite it
+                if tag in self.file_names:
+                    continue
+                f_name = os.path.join("./cache/cmc_files/MOTChallenge/", f_name)
+                self.file_names[tag] = f_name
+
+    def compute_affine(self, img, bbox, tag):
+        img = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
+        if tag in self.cache:
+            A = self.cache[tag]
+            return A
+        mask = np.ones_like(img, dtype=np.uint8)
+        if bbox.shape[0] > 0:
+            bbox = np.round(bbox).astype(np.int32)
+            bbox[bbox < 0] = 0
+            for bb in bbox:
+                mask[bb[1] : bb[3], bb[0] : bb[2]] = 0
+
+        A = self.comp_function(img, mask, tag)
+        self.cache[tag] = A
+
+        return A
+
+    def _affine_file(self, frame, mask, tag):
+        name, num = tag.split(":")
+        if name not in self.file_affines:
+            self._load_file(name)
+        if name not in self.file_affines:
+            raise RuntimeError("Error loading file affines for CMC.")
+
+        return self.file_affines[name][int(num) - 1]
+
+    def _affine_sift(self, frame, mask, tag):
+        A = np.eye(2, 3)
+        detector = cv2.SIFT_create()
+        kp, desc = detector.detectAndCompute(frame, mask)
+        if self.prev_desc is None:
+            self.prev_desc = [kp, desc]
+            return A
+        if desc.shape[0] < self.minimum_features or self.prev_desc[1].shape[0] < self.minimum_features:
+            return A
+
+        bf = cv2.BFMatcher(cv2.NORM_L2)
+        matches = bf.knnMatch(self.prev_desc[1], desc, k=2)
+        good = []
+        for m, n in matches:
+            if m.distance < 0.7 * n.distance:
+                good.append(m)
+
+        if len(good) > self.minimum_features:
+            src_pts = np.float32([self.prev_desc[0][m.queryIdx].pt for m in good]).reshape(-1, 1, 2)
+            dst_pts = np.float32([kp[m.trainIdx].pt for m in good]).reshape(-1, 1, 2)
+            A, _ = cv2.estimateAffinePartial2D(src_pts, dst_pts, method=cv2.RANSAC)
+        else:
+            print("Warning: not enough matching points")
+        if A is None:
+            A = np.eye(2, 3)
+
+        self.prev_desc = [kp, desc]
+        return A
+
+    def _affine_sparse_flow(self, frame, mask, tag):
+        # Initialize
+        A = np.eye(2, 3)
+
+        # find the keypoints
+        keypoints = cv2.goodFeaturesToTrack(frame, mask=mask, **self.sparse_flow_param)
+
+        # Handle first frame
+        if self.prev_img is None:
+            self.prev_img = frame
+            self.prev_desc = keypoints
+            return A
+
+        matched_kp, status, err = cv2.calcOpticalFlowPyrLK(self.prev_img, frame, self.prev_desc, None)
+        matched_kp = matched_kp.reshape(-1, 2)
+        status = status.reshape(-1)
+        prev_points = self.prev_desc.reshape(-1, 2)
+        prev_points = prev_points[status]
+        curr_points = matched_kp[status]
+
+        # Find rigid matrix
+        if prev_points.shape[0] > self.minimum_features:
+            A, _ = cv2.estimateAffinePartial2D(prev_points, curr_points, method=cv2.RANSAC)
+        else:
+            print("Warning: not enough matching points")
+        if A is None:
+            A = np.eye(2, 3)
+
+        self.prev_img = frame
+        self.prev_desc = keypoints
+        return A
+
+    def _load_file(self, name):
+        affines = []
+        with open(self.file_names[name], "r") as fp:
+            for line in fp:
+                tokens = [float(f) for f in line.split("\t")[1:7]]
+                A = np.eye(2, 3)
+                A[0, 0] = tokens[0]
+                A[0, 1] = tokens[1]
+                A[0, 2] = tokens[2]
+                A[1, 0] = tokens[3]
+                A[1, 1] = tokens[4]
+                A[1, 2] = tokens[5]
+                affines.append(A)
+        self.file_affines[name] = affines
+
+    def dump_cache(self):
+        return
+        with open(self.cache_path, "wb") as fp:
+            pickle.dump(self.cache, fp)
diff --git a/trackers/integrated_ocsort_embedding/embedding.py b/trackers/integrated_ocsort_embedding/embedding.py
new file mode 100644
index 0000000000000000000000000000000000000000..f5a6c65ff75db94600a90ffed9f98095b2f084c7
--- /dev/null
+++ b/trackers/integrated_ocsort_embedding/embedding.py
@@ -0,0 +1,201 @@
+from collections import OrderedDict
+from pathlib import Path
+import os
+import pickle
+
+import cv2
+import numpy as np
+
+
+class EmbeddingComputer:
+    def __init__(self, dataset, test_dataset, grid_off, max_batch=1024):
+        self.model = None
+        self.dataset = dataset
+        self.test_dataset = test_dataset
+        self.crop_size = (128, 384)
+        os.makedirs("./cache/embeddings/", exist_ok=True)
+        self.cache_path = "./cache/embeddings/{}_embedding.pkl"
+        self.cache = {}
+        self.cache_name = ""
+        self.grid_off = grid_off
+        self.max_batch = max_batch
+
+        # Only used for the general ReID model (not FastReID)
+        self.normalize = False
+
+    def load_cache(self, path):
+        self.cache_name = path
+        cache_path = self.cache_path.format(path)
+        if os.path.exists(cache_path):
+            with open(cache_path, "rb") as fp:
+                self.cache = pickle.load(fp)
+
+    def get_horizontal_split_patches(self, image, bbox, tag, idx, viz=False):
+        if isinstance(image, np.ndarray):
+            h, w = image.shape[:2]
+        else:
+            h, w = image.shape[2:]
+
+        bbox = np.array(bbox)
+        bbox = bbox.astype(np.int)
+        if bbox[0] < 0 or bbox[1] < 0 or bbox[2] > w or bbox[3] > h:
+            # Faulty Patch Correction
+            bbox[0] = np.clip(bbox[0], 0, None)
+            bbox[1] = np.clip(bbox[1], 0, None)
+            bbox[2] = np.clip(bbox[2], 0, image.shape[1])
+            bbox[3] = np.clip(bbox[3], 0, image.shape[0])
+
+        x1, y1, x2, y2 = bbox
+        w = x2 - x1
+        h = y2 - y1
+        ### TODO - Write a generalized split logic
+        split_boxes = [
+            [x1, y1, x1 + w, y1 + h / 3],
+            [x1, y1 + h / 3, x1 + w, y1 + (2 / 3) * h],
+            [x1, y1 + (2 / 3) * h, x1 + w, y1 + h],
+        ]
+
+        split_boxes = np.array(split_boxes, dtype="int")
+        patches = []
+        # breakpoint()
+        for ix, patch_coords in enumerate(split_boxes):
+            if isinstance(image, np.ndarray):
+                im1 = image[patch_coords[1] : patch_coords[3], patch_coords[0] : patch_coords[2], :]
+
+                if viz:  ## TODO - change it from torch tensor to numpy array
+                    dirs = "./viz/{}/{}".format(tag.split(":")[0], tag.split(":")[1])
+                    Path(dirs).mkdir(parents=True, exist_ok=True)
+                    cv2.imwrite(
+                        os.path.join(dirs, "{}_{}.png".format(idx, ix)),
+                        im1.squeeze(0).permute(1, 2, 0).detach().cpu().numpy() * 255,
+                    )
+                patch = cv2.cvtColor(im1, cv2.COLOR_BGR2RGB)
+                patch = cv2.resize(patch, self.crop_size, interpolation=cv2.INTER_LINEAR)
+                patch = torch.as_tensor(patch.astype("float32").transpose(2, 0, 1))
+                patch = patch.unsqueeze(0)
+                # print("test ", patch.shape)
+                patches.append(patch)
+            else:
+                im1 = image[:, :, patch_coords[1] : patch_coords[3], patch_coords[0] : patch_coords[2]]
+                patch = torchvision.transforms.functional.resize(im1, (256, 128))
+                patches.append(patch)
+
+        patches = torch.cat(patches, dim=0)
+
+        # print("Patches shape ", patches.shape)
+        # patches = np.array(patches)
+        # print("ALL SPLIT PATCHES SHAPE - ", patches.shape)
+
+        return patches
+
+    def compute_embedding(self, img, bbox, tag):
+        if self.cache_name != tag.split(":")[0]:
+            self.load_cache(tag.split(":")[0])
+
+        if tag in self.cache:
+            embs = self.cache[tag]
+            if embs.shape[0] != bbox.shape[0]:
+                raise RuntimeError(
+                    "ERROR: The number of cached embeddings don't match the "
+                    "number of detections.\nWas the detector model changed? Delete cache if so."
+                )
+            return embs
+
+        if self.model is None:
+            self.initialize_model()
+
+        # Generate all of the patches
+        crops = []
+        if self.grid_off:
+            # Basic embeddings
+            h, w = img.shape[:2]
+            results = np.round(bbox).astype(np.int32)
+            results[:, 0] = results[:, 0].clip(0, w)
+            results[:, 1] = results[:, 1].clip(0, h)
+            results[:, 2] = results[:, 2].clip(0, w)
+            results[:, 3] = results[:, 3].clip(0, h)
+
+            crops = []
+            for p in results:
+                crop = img[p[1] : p[3], p[0] : p[2]]
+                crop = cv2.cvtColor(crop, cv2.COLOR_BGR2RGB)
+                crop = cv2.resize(crop, self.crop_size, interpolation=cv2.INTER_LINEAR).astype(np.float32)
+                if self.normalize:
+                    crop /= 255
+                    crop -= np.array((0.485, 0.456, 0.406))
+                    crop /= np.array((0.229, 0.224, 0.225))
+                crop = torch.as_tensor(crop.transpose(2, 0, 1))
+                crop = crop.unsqueeze(0)
+                crops.append(crop)
+        else:
+            # Grid patch embeddings
+            for idx, box in enumerate(bbox):
+                crop = self.get_horizontal_split_patches(img, box, tag, idx)
+                crops.append(crop)
+        crops = torch.cat(crops, dim=0)
+
+        # Create embeddings and l2 normalize them
+        embs = []
+        for idx in range(0, len(crops), self.max_batch):
+            batch_crops = crops[idx : idx + self.max_batch]
+            batch_crops = batch_crops.cuda()
+            with torch.no_grad():
+                batch_embs = self.model(batch_crops)
+            embs.extend(batch_embs)
+        embs = torch.stack(embs)
+        embs = torch.nn.functional.normalize(embs, dim=-1)
+
+        if not self.grid_off:
+            embs = embs.reshape(bbox.shape[0], -1, embs.shape[-1])
+        embs = embs.cpu().numpy()
+
+        self.cache[tag] = embs
+        return embs
+
+    def initialize_model(self):
+        if self.dataset == "mot17":
+            if self.test_dataset:
+                path = "external/weights/mot17_sbs_S50.pth"
+            else:
+                return self._get_general_model()
+        elif self.dataset == "mot20":
+            if self.test_dataset:
+                path = "external/weights/mot20_sbs_S50.pth"
+            else:
+                return self._get_general_model()
+        elif self.dataset == "dance":
+            path = "external/weights/dance_sbs_S50.pth"
+        else:
+            raise RuntimeError("Need the path for a new ReID model.")
+
+        model = FastReID(path)
+        model.eval()
+        model.cuda()
+        model.half()
+        self.model = model
+
+    def _get_general_model(self):
+        """Used for the half-val for MOT17/20.
+
+        The MOT17/20 SBS models are trained over the half-val we
+        evaluate on as well. Instead we use a different model for
+        validation.
+        """
+        model = torchreid.models.build_model(name="osnet_ain_x1_0", num_classes=2510, loss="softmax", pretrained=False)
+        sd = torch.load("external/weights/osnet_ain_ms_d_c.pth.tar")["state_dict"]
+        new_state_dict = OrderedDict()
+        for k, v in sd.items():
+            name = k[7:]  # remove `module.`
+            new_state_dict[name] = v
+        # load params
+        model.load_state_dict(new_state_dict)
+        model.eval()
+        model.cuda()
+        self.model = model
+        self.crop_size = (128, 256)
+        self.normalize = True
+
+    def dump_cache(self):
+        if self.cache_name:
+            with open(self.cache_path.format(self.cache_name), "wb") as fp:
+                pickle.dump(self.cache, fp)
diff --git a/trackers/integrated_ocsort_embedding/kalmanfilter.py b/trackers/integrated_ocsort_embedding/kalmanfilter.py
new file mode 100644
index 0000000000000000000000000000000000000000..65412e13fdee46179ec878a83d0d59e92ba29279
--- /dev/null
+++ b/trackers/integrated_ocsort_embedding/kalmanfilter.py
@@ -0,0 +1,1646 @@
+# -*- coding: utf-8 -*-
+# pylint: disable=invalid-name, too-many-arguments, too-many-branches,
+# pylint: disable=too-many-locals, too-many-instance-attributes, too-many-lines
+
+"""
+This module implements the linear Kalman filter in both an object
+oriented and procedural form. The KalmanFilter class implements
+the filter by storing the various matrices in instance variables,
+minimizing the amount of bookkeeping you have to do.
+All Kalman filters operate with a predict->update cycle. The
+predict step, implemented with the method or function predict(),
+uses the state transition matrix F to predict the state in the next
+time period (epoch). The state is stored as a gaussian (x, P), where
+x is the state (column) vector, and P is its covariance. Covariance
+matrix Q specifies the process covariance. In Bayesian terms, this
+prediction is called the *prior*, which you can think of colloquially
+as the estimate prior to incorporating the measurement.
+The update step, implemented with the method or function `update()`,
+incorporates the measurement z with covariance R, into the state
+estimate (x, P). The class stores the system uncertainty in S,
+the innovation (residual between prediction and measurement in
+measurement space) in y, and the Kalman gain in k. The procedural
+form returns these variables to you. In Bayesian terms this computes
+the *posterior* - the estimate after the information from the
+measurement is incorporated.
+Whether you use the OO form or procedural form is up to you. If
+matrices such as H, R, and F are changing each epoch, you'll probably
+opt to use the procedural form. If they are unchanging, the OO
+form is perhaps easier to use since you won't need to keep track
+of these matrices. This is especially useful if you are implementing
+banks of filters or comparing various KF designs for performance;
+a trivial coding bug could lead to using the wrong sets of matrices.
+This module also offers an implementation of the RTS smoother, and
+other helper functions, such as log likelihood computations.
+The Saver class allows you to easily save the state of the
+KalmanFilter class after every update
+This module expects NumPy arrays for all values that expect
+arrays, although in a few cases, particularly method parameters,
+it will accept types that convert to NumPy arrays, such as lists
+of lists. These exceptions are documented in the method or function.
+Examples
+--------
+The following example constructs a constant velocity kinematic
+filter, filters noisy data, and plots the results. It also demonstrates
+using the Saver class to save the state of the filter at each epoch.
+.. code-block:: Python
+    import matplotlib.pyplot as plt
+    import numpy as np
+    from filterpy.kalman import KalmanFilter
+    from filterpy.common import Q_discrete_white_noise, Saver
+    r_std, q_std = 2., 0.003
+    cv = KalmanFilter(dim_x=2, dim_z=1)
+    cv.x = np.array([[0., 1.]]) # position, velocity
+    cv.F = np.array([[1, dt],[ [0, 1]])
+    cv.R = np.array([[r_std^^2]])
+    f.H = np.array([[1., 0.]])
+    f.P = np.diag([.1^^2, .03^^2)
+    f.Q = Q_discrete_white_noise(2, dt, q_std**2)
+    saver = Saver(cv)
+    for z in range(100):
+        cv.predict()
+        cv.update([z + randn() * r_std])
+        saver.save() # save the filter's state
+    saver.to_array()
+    plt.plot(saver.x[:, 0])
+    # plot all of the priors
+    plt.plot(saver.x_prior[:, 0])
+    # plot mahalanobis distance
+    plt.figure()
+    plt.plot(saver.mahalanobis)
+This code implements the same filter using the procedural form
+    x = np.array([[0., 1.]]) # position, velocity
+    F = np.array([[1, dt],[ [0, 1]])
+    R = np.array([[r_std^^2]])
+    H = np.array([[1., 0.]])
+    P = np.diag([.1^^2, .03^^2)
+    Q = Q_discrete_white_noise(2, dt, q_std**2)
+    for z in range(100):
+        x, P = predict(x, P, F=F, Q=Q)
+        x, P = update(x, P, z=[z + randn() * r_std], R=R, H=H)
+        xs.append(x[0, 0])
+    plt.plot(xs)
+For more examples see the test subdirectory, or refer to the
+book cited below. In it I both teach Kalman filtering from basic
+principles, and teach the use of this library in great detail.
+FilterPy library.
+http://github.com/rlabbe/filterpy
+Documentation at:
+https://filterpy.readthedocs.org
+Supporting book at:
+https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+This is licensed under an MIT license. See the readme.MD file
+for more information.
+Copyright 2014-2018 Roger R Labbe Jr.
+"""
+
+from __future__ import absolute_import, division
+
+import pdb
+from copy import deepcopy
+from math import log, exp, sqrt
+import sys
+import numpy as np
+from numpy import dot, zeros, eye, isscalar, shape
+import numpy.linalg as linalg
+from filterpy.stats import logpdf
+from filterpy.common import pretty_str, reshape_z
+
+
+class KalmanFilterNew(object):
+    """Implements a Kalman filter. You are responsible for setting the
+    various state variables to reasonable values; the defaults  will
+    not give you a functional filter.
+    For now the best documentation is my free book Kalman and Bayesian
+    Filters in Python [2]_. The test files in this directory also give you a
+    basic idea of use, albeit without much description.
+    In brief, you will first construct this object, specifying the size of
+    the state vector with dim_x and the size of the measurement vector that
+    you will be using with dim_z. These are mostly used to perform size checks
+    when you assign values to the various matrices. For example, if you
+    specified dim_z=2 and then try to assign a 3x3 matrix to R (the
+    measurement noise matrix you will get an assert exception because R
+    should be 2x2. (If for whatever reason you need to alter the size of
+    things midstream just use the underscore version of the matrices to
+    assign directly: your_filter._R = a_3x3_matrix.)
+    After construction the filter will have default matrices created for you,
+    but you must specify the values for each. It’s usually easiest to just
+    overwrite them rather than assign to each element yourself. This will be
+    clearer in the example below. All are of type numpy.array.
+    Examples
+    --------
+    Here is a filter that tracks position and velocity using a sensor that only
+    reads position.
+    First construct the object with the required dimensionality. Here the state
+    (`dim_x`) has 2 coefficients (position and velocity), and the measurement
+    (`dim_z`) has one. In FilterPy `x` is the state, `z` is the measurement.
+    .. code::
+        from filterpy.kalman import KalmanFilter
+        f = KalmanFilter (dim_x=2, dim_z=1)
+    Assign the initial value for the state (position and velocity). You can do this
+    with a two dimensional array like so:
+        .. code::
+            f.x = np.array([[2.],    # position
+                            [0.]])   # velocity
+    or just use a one dimensional array, which I prefer doing.
+    .. code::
+        f.x = np.array([2., 0.])
+    Define the state transition matrix:
+        .. code::
+            f.F = np.array([[1.,1.],
+                            [0.,1.]])
+    Define the measurement function. Here we need to convert a position-velocity
+    vector into just a position vector, so we use:
+        .. code::
+        f.H = np.array([[1., 0.]])
+    Define the state's covariance matrix P.
+    .. code::
+        f.P = np.array([[1000.,    0.],
+                        [   0., 1000.] ])
+    Now assign the measurement noise. Here the dimension is 1x1, so I can
+    use a scalar
+    .. code::
+        f.R = 5
+    I could have done this instead:
+    .. code::
+        f.R = np.array([[5.]])
+    Note that this must be a 2 dimensional array.
+    Finally, I will assign the process noise. Here I will take advantage of
+    another FilterPy library function:
+    .. code::
+        from filterpy.common import Q_discrete_white_noise
+        f.Q = Q_discrete_white_noise(dim=2, dt=0.1, var=0.13)
+    Now just perform the standard predict/update loop:
+    .. code::
+        while some_condition_is_true:
+            z = get_sensor_reading()
+            f.predict()
+            f.update(z)
+            do_something_with_estimate (f.x)
+    **Procedural Form**
+    This module also contains stand alone functions to perform Kalman filtering.
+    Use these if you are not a fan of objects.
+    **Example**
+    .. code::
+        while True:
+            z, R = read_sensor()
+            x, P = predict(x, P, F, Q)
+            x, P = update(x, P, z, R, H)
+    See my book Kalman and Bayesian Filters in Python [2]_.
+    You will have to set the following attributes after constructing this
+    object for the filter to perform properly. Please note that there are
+    various checks in place to ensure that you have made everything the
+    'correct' size. However, it is possible to provide incorrectly sized
+    arrays such that the linear algebra can not perform an operation.
+    It can also fail silently - you can end up with matrices of a size that
+    allows the linear algebra to work, but are the wrong shape for the problem
+    you are trying to solve.
+    Parameters
+    ----------
+    dim_x : int
+        Number of state variables for the Kalman filter. For example, if
+        you are tracking the position and velocity of an object in two
+        dimensions, dim_x would be 4.
+        This is used to set the default size of P, Q, and u
+    dim_z : int
+        Number of of measurement inputs. For example, if the sensor
+        provides you with position in (x,y), dim_z would be 2.
+    dim_u : int (optional)
+        size of the control input, if it is being used.
+        Default value of 0 indicates it is not used.
+    compute_log_likelihood : bool (default = True)
+        Computes log likelihood by default, but this can be a slow
+        computation, so if you never use it you can turn this computation
+        off.
+    Attributes
+    ----------
+    x : numpy.array(dim_x, 1)
+        Current state estimate. Any call to update() or predict() updates
+        this variable.
+    P : numpy.array(dim_x, dim_x)
+        Current state covariance matrix. Any call to update() or predict()
+        updates this variable.
+    x_prior : numpy.array(dim_x, 1)
+        Prior (predicted) state estimate. The *_prior and *_post attributes
+        are for convenience; they store the  prior and posterior of the
+        current epoch. Read Only.
+    P_prior : numpy.array(dim_x, dim_x)
+        Prior (predicted) state covariance matrix. Read Only.
+    x_post : numpy.array(dim_x, 1)
+        Posterior (updated) state estimate. Read Only.
+    P_post : numpy.array(dim_x, dim_x)
+        Posterior (updated) state covariance matrix. Read Only.
+    z : numpy.array
+        Last measurement used in update(). Read only.
+    R : numpy.array(dim_z, dim_z)
+        Measurement noise covariance matrix. Also known as the
+        observation covariance.
+    Q : numpy.array(dim_x, dim_x)
+        Process noise covariance matrix. Also known as the transition
+        covariance.
+    F : numpy.array()
+        State Transition matrix. Also known as `A` in some formulation.
+    H : numpy.array(dim_z, dim_x)
+        Measurement function. Also known as the observation matrix, or as `C`.
+    y : numpy.array
+        Residual of the update step. Read only.
+    K : numpy.array(dim_x, dim_z)
+        Kalman gain of the update step. Read only.
+    S :  numpy.array
+        System uncertainty (P projected to measurement space). Read only.
+    SI :  numpy.array
+        Inverse system uncertainty. Read only.
+    log_likelihood : float
+        log-likelihood of the last measurement. Read only.
+    likelihood : float
+        likelihood of last measurement. Read only.
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+    mahalanobis : float
+        mahalanobis distance of the innovation. Read only.
+    inv : function, default numpy.linalg.inv
+        If you prefer another inverse function, such as the Moore-Penrose
+        pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        This is only used to invert self.S. If you know it is diagonal, you
+        might choose to set it to filterpy.common.inv_diagonal, which is
+        several times faster than numpy.linalg.inv for diagonal matrices.
+    alpha : float
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+    References
+    ----------
+    .. [1] Dan Simon. "Optimal State Estimation." John Wiley & Sons.
+       p. 208-212. (2006)
+    .. [2] Roger Labbe. "Kalman and Bayesian Filters in Python"
+       https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
+    """
+
+    def __init__(self, dim_x, dim_z, dim_u=0):
+        if dim_x < 1:
+            raise ValueError("dim_x must be 1 or greater")
+        if dim_z < 1:
+            raise ValueError("dim_z must be 1 or greater")
+        if dim_u < 0:
+            raise ValueError("dim_u must be 0 or greater")
+
+        self.dim_x = dim_x
+        self.dim_z = dim_z
+        self.dim_u = dim_u
+
+        self.x = zeros((dim_x, 1))  # state
+        self.P = eye(dim_x)  # uncertainty covariance
+        self.Q = eye(dim_x)  # process uncertainty
+        self.B = None  # control transition matrix
+        self.F = eye(dim_x)  # state transition matrix
+        self.H = zeros((dim_z, dim_x))  # measurement function
+        self.R = eye(dim_z)  # measurement uncertainty
+        self._alpha_sq = 1.0  # fading memory control
+        self.M = np.zeros((dim_x, dim_z))  # process-measurement cross correlation
+        self.z = np.array([[None] * self.dim_z]).T
+
+        # gain and residual are computed during the innovation step. We
+        # save them so that in case you want to inspect them for various
+        # purposes
+        self.K = np.zeros((dim_x, dim_z))  # kalman gain
+        self.y = zeros((dim_z, 1))
+        self.S = np.zeros((dim_z, dim_z))  # system uncertainty
+        self.SI = np.zeros((dim_z, dim_z))  # inverse system uncertainty
+
+        # identity matrix. Do not alter this.
+        self._I = np.eye(dim_x)
+
+        # these will always be a copy of x,P after predict() is called
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+        # these will always be a copy of x,P after update() is called
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+        # Only computed only if requested via property
+        self._log_likelihood = log(sys.float_info.min)
+        self._likelihood = sys.float_info.min
+        self._mahalanobis = None
+
+        # keep all observations
+        self.history_obs = []
+
+        self.inv = np.linalg.inv
+
+        self.attr_saved = None
+        self.observed = False
+        self.last_measurement = None
+
+    def predict(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            self.x = dot(F, self.x) + dot(B, u)
+        else:
+            self.x = dot(F, self.x)
+
+        # P = FPF' + Q
+        self.P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+    def freeze(self):
+        """
+        Save the parameters before non-observation forward
+        """
+        self.attr_saved = deepcopy(self.__dict__)
+
+    def apply_affine_correction(self, m, t, new_kf):
+        """
+        Apply to both last state and last observation for OOS smoothing.
+
+        Messy due to internal logic for kalman filter being messy.
+        """
+        if new_kf:
+            big_m = np.kron(np.eye(4, dtype=float), m)
+            self.x = big_m @ self.x
+            self.x[:2] += t
+            self.P = big_m @ self.P @ big_m.T
+
+            # If frozen, also need to update the frozen state for OOS
+            if not self.observed and self.attr_saved is not None:
+                self.attr_saved["x"] = big_m @ self.attr_saved["x"]
+                self.attr_saved["x"][:2] += t
+                self.attr_saved["P"] = big_m @ self.attr_saved["P"] @ big_m.T
+                self.attr_saved["last_measurement"][:2] = m @ self.attr_saved["last_measurement"][:2] + t
+                self.attr_saved["last_measurement"][2:] = m @ self.attr_saved["last_measurement"][2:]
+        else:
+            scale = np.linalg.norm(m[:, 0])
+            self.x[:2] = m @ self.x[:2] + t
+            self.x[4:6] = m @ self.x[4:6]
+            # self.x[2] *= scale
+            # self.x[6] *= scale
+
+            self.P[:2, :2] = m @ self.P[:2, :2] @ m.T
+            self.P[4:6, 4:6] = m @ self.P[4:6, 4:6] @ m.T
+            # self.P[2, 2] *= 2 * scale
+            # self.P[6, 6] *= 2 * scale
+
+            # If frozen, also need to update the frozen state for OOS
+            if not self.observed and self.attr_saved is not None:
+                self.attr_saved["x"][:2] = m @ self.attr_saved["x"][:2] + t
+                self.attr_saved["x"][4:6] = m @ self.attr_saved["x"][4:6]
+                # self.attr_saved["x"][2] *= scale
+                # self.attr_saved["x"][6] *= scale
+
+                self.attr_saved["P"][:2, :2] = m @ self.attr_saved["P"][:2, :2] @ m.T
+                self.attr_saved["P"][4:6, 4:6] = m @ self.attr_saved["P"][4:6, 4:6] @ m.T
+                # self.attr_saved["P"][2, 2] *= 2 * scale
+                # self.attr_saved["P"][6, 6] *= 2 * scale
+
+                self.attr_saved["last_measurement"][:2] = m @ self.attr_saved["last_measurement"][:2] + t
+                # self.attr_saved["last_measurement"][2] *= scale
+
+    def unfreeze(self, new_kf):
+        if self.attr_saved is not None:
+            new_history = deepcopy(self.history_obs)
+            self.__dict__ = self.attr_saved
+            # self.history_obs = new_history
+            self.history_obs = self.history_obs[:-1]
+            occur = [int(d is None) for d in new_history]
+            indices = np.where(np.array(occur) == 0)[0]
+            index1 = indices[-2]
+            index2 = indices[-1]
+            # box1 = new_history[index1]
+            box1 = self.last_measurement
+            if new_kf:
+                x1, y1, w1, h1 = box1
+            else:
+                x1, y1, s1, r1 = box1
+                w1 = np.sqrt(s1 * r1)
+                h1 = np.sqrt(s1 / r1)
+            box2 = new_history[index2]
+            if new_kf:
+                x2, y2, w2, h2 = box2
+            else:
+                x2, y2, s2, r2 = box2
+                w2 = np.sqrt(s2 * r2)
+                h2 = np.sqrt(s2 / r2)
+            time_gap = index2 - index1
+            dx = (x2 - x1) / time_gap
+            dy = (y2 - y1) / time_gap
+            dw = (w2 - w1) / time_gap
+            dh = (h2 - h1) / time_gap
+            for i in range(index2 - index1):
+                """
+                The default virtual trajectory generation is by linear
+                motion (constant speed hypothesis), you could modify this
+                part to implement your own.
+                """
+                x = x1 + (i + 1) * dx
+                y = y1 + (i + 1) * dy
+                w = w1 + (i + 1) * dw
+                h = h1 + (i + 1) * dh
+                if new_kf:
+                    new_box = np.array([x, y, w, h]).reshape((4, 1))
+                else:
+                    s = w * h
+                    r = w / float(h)
+                    new_box = np.array([x, y, s, r]).reshape((4, 1))
+                """
+                    I still use predict-update loop here to refresh the parameters,
+                    but this can be faster by directly modifying the internal parameters
+                    as suggested in the paper. I keep this naive but slow way for 
+                    easy read and understanding
+                """
+                self.update(new_box)
+                if not i == (index2 - index1 - 1):
+                    self.predict()
+
+    def update(self, z, R=None, H=None, new_kf=False):
+        """
+        Add a new measurement (z) to the Kalman filter.
+        If z is None, nothing is computed. However, x_post and P_post are
+        updated with the prior (x_prior, P_prior), and self.z is set to None.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+            If you pass in a value of H, z must be a column vector the
+            of the correct size.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array, or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise self.H will be used.
+        """
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        # append the observation
+        self.history_obs.append(z)
+
+        if z is None:
+            if self.observed:
+                """
+                Got no observation so freeze the current parameters for future
+                potential online smoothing.
+                """
+                self.last_measurement = self.history_obs[-2]
+                self.freeze()
+            self.observed = False
+            self.z = np.array([[None] * self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        # self.observed = True
+        if not self.observed:
+            """
+            Get observation, use online smoothing to re-update parameters
+            """
+            self.unfreeze(new_kf)
+        self.observed = True
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # S = HPH' + R
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + R
+        self.SI = self.inv(self.S)
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        # This is more numerically stable
+        # and works for non-optimal K vs the equation
+        # P = (I-KH)P usually seen in the literature.
+
+        I_KH = self._I - dot(self.K, H)
+        self.P = dot(dot(I_KH, self.P), I_KH.T) + dot(dot(self.K, R), self.K.T)
+
+        # save measurement and posterior state
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def md_for_measurement(self, z):
+        """Mahalanobis distance for any measurement.
+
+
+        self._mahalanobis = sqrt(float(dot(dot(self.y.T, self.SI), self.y)))
+
+        Should be run after a prediction() call.
+        """
+        y = z - self.H @ self.x
+        md = float(dot(dot(y.T, self.SI), y))
+        return md
+
+    def predict_steadystate(self, u=0, B=None):
+        """
+        Predict state (prior) using the Kalman filter state propagation
+        equations. Only x is updated, P is left unchanged. See
+        update_steadstate() for a longer explanation of when to use this
+        method.
+        Parameters
+        ----------
+        u : np.array
+            Optional control vector. If non-zero, it is multiplied by B
+            to create the control input into the system.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        """
+
+        if B is None:
+            B = self.B
+
+        # x = Fx + Bu
+        if B is not None:
+            self.x = dot(self.F, self.x) + dot(B, u)
+        else:
+            self.x = dot(self.F, self.x)
+
+        # save prior
+        self.x_prior = self.x.copy()
+        self.P_prior = self.P.copy()
+
+    def update_steadystate(self, z):
+        """
+        Add a new measurement (z) to the Kalman filter without recomputing
+        the Kalman gain K, the state covariance P, or the system
+        uncertainty S.
+        You can use this for LTI systems since the Kalman gain and covariance
+        converge to a fixed value. Precompute these and assign them explicitly,
+        or run the Kalman filter using the normal predict()/update(0 cycle
+        until they converge.
+        The main advantage of this call is speed. We do significantly less
+        computation, notably avoiding a costly matrix inversion.
+        Use in conjunction with predict_steadystate(), otherwise P will grow
+        without bound.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Examples
+        --------
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> # let filter converge on representative data, then save k and P
+        >>> for i in range(100):
+        >>>     cv.predict()
+        >>>     cv.update([i, i, i])
+        >>> saved_k = np.copy(cv.K)
+        >>> saved_P = np.copy(cv.P)
+        later on:
+        >>> cv = kinematic_kf(dim=3, order=2) # 3D const velocity filter
+        >>> cv.K = np.copy(saved_K)
+        >>> cv.P = np.copy(saved_P)
+        >>> for i in range(100):
+        >>>     cv.predict_steadystate()
+        >>>     cv.update_steadystate([i, i, i])
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None] * self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(self.H, self.x)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+    def update_correlated(self, z, R=None, H=None):
+        """Add a new measurement (z) to the Kalman filter assuming that
+        process noise and measurement noise are correlated as defined in
+        the `self.M` matrix.
+        A partial derivation can be found in [1]
+        If z is None, nothing is changed.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        R : np.array, scalar, or None
+            Optionally provide R to override the measurement noise for this
+            one call, otherwise  self.R will be used.
+        H : np.array,  or None
+            Optionally provide H to override the measurement function for this
+            one call, otherwise  self.H will be used.
+        References
+        ----------
+        .. [1] Bulut, Y. (2011). Applied Kalman filter theory (Doctoral dissertation, Northeastern University).
+               http://people.duke.edu/~hpgavin/SystemID/References/Balut-KalmanFilter-PhD-NEU-2011.pdf
+        """
+
+        # set to None to force recompute
+        self._log_likelihood = None
+        self._likelihood = None
+        self._mahalanobis = None
+
+        if z is None:
+            self.z = np.array([[None] * self.dim_z]).T
+            self.x_post = self.x.copy()
+            self.P_post = self.P.copy()
+            self.y = zeros((self.dim_z, 1))
+            return
+
+        if R is None:
+            R = self.R
+        elif isscalar(R):
+            R = eye(self.dim_z) * R
+
+        # rename for readability and a tiny extra bit of speed
+        if H is None:
+            z = reshape_z(z, self.dim_z, self.x.ndim)
+            H = self.H
+
+        # handle special case: if z is in form [[z]] but x is not a column
+        # vector dimensions will not match
+        if self.x.ndim == 1 and shape(z) == (1, 1):
+            z = z[0]
+
+        if shape(z) == ():  # is it scalar, e.g. z=3 or z=np.array(3)
+            z = np.asarray([z])
+
+        # y = z - Hx
+        # error (residual) between measurement and prediction
+        self.y = z - dot(H, self.x)
+
+        # common subexpression for speed
+        PHT = dot(self.P, H.T)
+
+        # project system uncertainty into measurement space
+        self.S = dot(H, PHT) + dot(H, self.M) + dot(self.M.T, H.T) + R
+        self.SI = self.inv(self.S)
+
+        # K = PH'inv(S)
+        # map system uncertainty into kalman gain
+        self.K = dot(PHT + self.M, self.SI)
+
+        # x = x + Ky
+        # predict new x with residual scaled by the kalman gain
+        self.x = self.x + dot(self.K, self.y)
+        self.P = self.P - dot(self.K, dot(H, self.P) + self.M.T)
+
+        self.z = deepcopy(z)
+        self.x_post = self.x.copy()
+        self.P_post = self.P.copy()
+
+    def batch_filter(
+        self,
+        zs,
+        Fs=None,
+        Qs=None,
+        Hs=None,
+        Rs=None,
+        Bs=None,
+        us=None,
+        update_first=False,
+        saver=None,
+    ):
+        """Batch processes a sequences of measurements.
+         Parameters
+         ----------
+         zs : list-like
+             list of measurements at each time step `self.dt`. Missing
+             measurements must be represented by `None`.
+         Fs : None, list-like, default=None
+             optional value or list of values to use for the state transition
+             matrix F.
+             If Fs is None then self.F is used for all epochs.
+             Otherwise it must contain a list-like list of F's, one for
+             each epoch.  This allows you to have varying F per epoch.
+         Qs : None, np.array or list-like, default=None
+             optional value or list of values to use for the process error
+             covariance Q.
+             If Qs is None then self.Q is used for all epochs.
+             Otherwise it must contain a list-like list of Q's, one for
+             each epoch.  This allows you to have varying Q per epoch.
+         Hs : None, np.array or list-like, default=None
+             optional list of values to use for the measurement matrix H.
+             If Hs is None then self.H is used for all epochs.
+             If Hs contains a single matrix, then it is used as H for all
+             epochs.
+             Otherwise it must contain a list-like list of H's, one for
+             each epoch.  This allows you to have varying H per epoch.
+         Rs : None, np.array or list-like, default=None
+             optional list of values to use for the measurement error
+             covariance R.
+             If Rs is None then self.R is used for all epochs.
+             Otherwise it must contain a list-like list of R's, one for
+             each epoch.  This allows you to have varying R per epoch.
+         Bs : None, np.array or list-like, default=None
+             optional list of values to use for the control transition matrix B.
+             If Bs is None then self.B is used for all epochs.
+             Otherwise it must contain a list-like list of B's, one for
+             each epoch.  This allows you to have varying B per epoch.
+         us : None, np.array or list-like, default=None
+             optional list of values to use for the control input vector;
+             If us is None then None is used for all epochs (equivalent to 0,
+             or no control input).
+             Otherwise it must contain a list-like list of u's, one for
+             each epoch.
+        update_first : bool, optional, default=False
+             controls whether the order of operations is update followed by
+             predict, or predict followed by update. Default is predict->update.
+         saver : filterpy.common.Saver, optional
+             filterpy.common.Saver object. If provided, saver.save() will be
+             called after every epoch
+         Returns
+         -------
+         means : np.array((n,dim_x,1))
+             array of the state for each time step after the update. Each entry
+             is an np.array. In other words `means[k,:]` is the state at step
+             `k`.
+         covariance : np.array((n,dim_x,dim_x))
+             array of the covariances for each time step after the update.
+             In other words `covariance[k,:,:]` is the covariance at step `k`.
+         means_predictions : np.array((n,dim_x,1))
+             array of the state for each time step after the predictions. Each
+             entry is an np.array. In other words `means[k,:]` is the state at
+             step `k`.
+         covariance_predictions : np.array((n,dim_x,dim_x))
+             array of the covariances for each time step after the prediction.
+             In other words `covariance[k,:,:]` is the covariance at step `k`.
+         Examples
+         --------
+         .. code-block:: Python
+             # this example demonstrates tracking a measurement where the time
+             # between measurement varies, as stored in dts. This requires
+             # that F be recomputed for each epoch. The output is then smoothed
+             # with an RTS smoother.
+             zs = [t + random.randn()*4 for t in range (40)]
+             Fs = [np.array([[1., dt], [0, 1]] for dt in dts]
+             (mu, cov, _, _) = kf.batch_filter(zs, Fs=Fs)
+             (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs)
+        """
+
+        # pylint: disable=too-many-statements
+        n = np.size(zs, 0)
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+        if Hs is None:
+            Hs = [self.H] * n
+        if Rs is None:
+            Rs = [self.R] * n
+        if Bs is None:
+            Bs = [self.B] * n
+        if us is None:
+            us = [0] * n
+
+        # mean estimates from Kalman Filter
+        if self.x.ndim == 1:
+            means = zeros((n, self.dim_x))
+            means_p = zeros((n, self.dim_x))
+        else:
+            means = zeros((n, self.dim_x, 1))
+            means_p = zeros((n, self.dim_x, 1))
+
+        # state covariances from Kalman Filter
+        covariances = zeros((n, self.dim_x, self.dim_x))
+        covariances_p = zeros((n, self.dim_x, self.dim_x))
+
+        if update_first:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+        else:
+            for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+                self.predict(u=u, B=B, F=F, Q=Q)
+                means_p[i, :] = self.x
+                covariances_p[i, :, :] = self.P
+
+                self.update(z, R=R, H=H)
+                means[i, :] = self.x
+                covariances[i, :, :] = self.P
+
+                if saver is not None:
+                    saver.save()
+
+        return (means, covariances, means_p, covariances_p)
+
+    def rts_smoother(self, Xs, Ps, Fs=None, Qs=None, inv=np.linalg.inv):
+        """
+        Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+        means and covariances computed by a Kalman filter. The usual input
+        would come from the output of `KalmanFilter.batch_filter()`.
+        Parameters
+        ----------
+        Xs : numpy.array
+           array of the means (state variable x) of the output of a Kalman
+           filter.
+        Ps : numpy.array
+            array of the covariances of the output of a kalman filter.
+        Fs : list-like collection of numpy.array, optional
+            State transition matrix of the Kalman filter at each time step.
+            Optional, if not provided the filter's self.F will be used
+        Qs : list-like collection of numpy.array, optional
+            Process noise of the Kalman filter at each time step. Optional,
+            if not provided the filter's self.Q will be used
+        inv : function, default numpy.linalg.inv
+            If you prefer another inverse function, such as the Moore-Penrose
+            pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
+        Returns
+        -------
+        x : numpy.ndarray
+           smoothed means
+        P : numpy.ndarray
+           smoothed state covariances
+        K : numpy.ndarray
+            smoother gain at each step
+        Pp : numpy.ndarray
+           Predicted state covariances
+        Examples
+        --------
+        .. code-block:: Python
+            zs = [t + random.randn()*4 for t in range (40)]
+            (mu, cov, _, _) = kalman.batch_filter(zs)
+            (x, P, K, Pp) = rts_smoother(mu, cov, kf.F, kf.Q)
+        """
+
+        if len(Xs) != len(Ps):
+            raise ValueError("length of Xs and Ps must be the same")
+
+        n = Xs.shape[0]
+        dim_x = Xs.shape[1]
+
+        if Fs is None:
+            Fs = [self.F] * n
+        if Qs is None:
+            Qs = [self.Q] * n
+
+        # smoother gain
+        K = zeros((n, dim_x, dim_x))
+
+        x, P, Pp = Xs.copy(), Ps.copy(), Ps.copy()
+        for k in range(n - 2, -1, -1):
+            Pp[k] = dot(dot(Fs[k + 1], P[k]), Fs[k + 1].T) + Qs[k + 1]
+
+            # pylint: disable=bad-whitespace
+            K[k] = dot(dot(P[k], Fs[k + 1].T), inv(Pp[k]))
+            x[k] += dot(K[k], x[k + 1] - dot(Fs[k + 1], x[k]))
+            P[k] += dot(dot(K[k], P[k + 1] - Pp[k]), K[k].T)
+
+        return (x, P, K, Pp)
+
+    def get_prediction(self, u=None, B=None, F=None, Q=None):
+        """
+        Predict next state (prior) using the Kalman filter state propagation
+        equations and returns it without modifying the object.
+        Parameters
+        ----------
+        u : np.array, default 0
+            Optional control vector.
+        B : np.array(dim_x, dim_u), or None
+            Optional control transition matrix; a value of None
+            will cause the filter to use `self.B`.
+        F : np.array(dim_x, dim_x), or None
+            Optional state transition matrix; a value of None
+            will cause the filter to use `self.F`.
+        Q : np.array(dim_x, dim_x), scalar, or None
+            Optional process noise matrix; a value of None will cause the
+            filter to use `self.Q`.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the prediction.
+        """
+
+        if B is None:
+            B = self.B
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        elif isscalar(Q):
+            Q = eye(self.dim_x) * Q
+
+        # x = Fx + Bu
+        if B is not None and u is not None:
+            x = dot(F, self.x) + dot(B, u)
+        else:
+            x = dot(F, self.x)
+
+        # P = FPF' + Q
+        P = self._alpha_sq * dot(dot(F, self.P), F.T) + Q
+
+        return x, P
+
+    def get_update(self, z=None):
+        """
+        Computes the new estimate based on measurement `z` and returns it
+        without altering the state of the filter.
+        Parameters
+        ----------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        Returns
+        -------
+        (x, P) : tuple
+            State vector and covariance array of the update.
+        """
+
+        if z is None:
+            return self.x, self.P
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+
+        R = self.R
+        H = self.H
+        P = self.P
+        x = self.x
+
+        # error (residual) between measurement and prediction
+        y = z - dot(H, x)
+
+        # common subexpression for speed
+        PHT = dot(P, H.T)
+
+        # project system uncertainty into measurement space
+        S = dot(H, PHT) + R
+
+        # map system uncertainty into kalman gain
+        K = dot(PHT, self.inv(S))
+
+        # predict new x with residual scaled by the kalman gain
+        x = x + dot(K, y)
+
+        # P = (I-KH)P(I-KH)' + KRK'
+        I_KH = self._I - dot(K, H)
+        P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+        return x, P
+
+    def residual_of(self, z):
+        """
+        Returns the residual for the given measurement (z). Does not alter
+        the state of the filter.
+        """
+        z = reshape_z(z, self.dim_z, self.x.ndim)
+        return z - dot(self.H, self.x_prior)
+
+    def measurement_of_state(self, x):
+        """
+        Helper function that converts a state into a measurement.
+        Parameters
+        ----------
+        x : np.array
+            kalman state vector
+        Returns
+        -------
+        z : (dim_z, 1): array_like
+            measurement for this update. z can be a scalar if dim_z is 1,
+            otherwise it must be convertible to a column vector.
+        """
+
+        return dot(self.H, x)
+
+    @property
+    def log_likelihood(self):
+        """
+        log-likelihood of the last measurement.
+        """
+        if self._log_likelihood is None:
+            self._log_likelihood = logpdf(x=self.y, cov=self.S)
+        return self._log_likelihood
+
+    @property
+    def likelihood(self):
+        """
+        Computed from the log-likelihood. The log-likelihood can be very
+        small,  meaning a large negative value such as -28000. Taking the
+        exp() of that results in 0.0, which can break typical algorithms
+        which multiply by this value, so by default we always return a
+        number >= sys.float_info.min.
+        """
+        if self._likelihood is None:
+            self._likelihood = exp(self.log_likelihood)
+            if self._likelihood == 0:
+                self._likelihood = sys.float_info.min
+        return self._likelihood
+
+    @property
+    def mahalanobis(self):
+        """ "
+        Mahalanobis distance of measurement. E.g. 3 means measurement
+        was 3 standard deviations away from the predicted value.
+        Returns
+        -------
+        mahalanobis : float
+        """
+        if self._mahalanobis is None:
+            self._mahalanobis = sqrt(float(dot(dot(self.y.T, self.SI), self.y)))
+        return self._mahalanobis
+
+    @property
+    def alpha(self):
+        """
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon [1]_.
+        """
+        return self._alpha_sq**0.5
+
+    def log_likelihood_of(self, z):
+        """
+        log likelihood of the measurement `z`. This should only be called
+        after a call to update(). Calling after predict() will yield an
+        incorrect result."""
+
+        if z is None:
+            return log(sys.float_info.min)
+        return logpdf(z, dot(self.H, self.x), self.S)
+
+    @alpha.setter
+    def alpha(self, value):
+        if not np.isscalar(value) or value < 1:
+            raise ValueError("alpha must be a float greater than 1")
+
+        self._alpha_sq = value**2
+
+    def __repr__(self):
+        return "\n".join(
+            [
+                "KalmanFilter object",
+                pretty_str("dim_x", self.dim_x),
+                pretty_str("dim_z", self.dim_z),
+                pretty_str("dim_u", self.dim_u),
+                pretty_str("x", self.x),
+                pretty_str("P", self.P),
+                pretty_str("x_prior", self.x_prior),
+                pretty_str("P_prior", self.P_prior),
+                pretty_str("x_post", self.x_post),
+                pretty_str("P_post", self.P_post),
+                pretty_str("F", self.F),
+                pretty_str("Q", self.Q),
+                pretty_str("R", self.R),
+                pretty_str("H", self.H),
+                pretty_str("K", self.K),
+                pretty_str("y", self.y),
+                pretty_str("S", self.S),
+                pretty_str("SI", self.SI),
+                pretty_str("M", self.M),
+                pretty_str("B", self.B),
+                pretty_str("z", self.z),
+                pretty_str("log-likelihood", self.log_likelihood),
+                pretty_str("likelihood", self.likelihood),
+                pretty_str("mahalanobis", self.mahalanobis),
+                pretty_str("alpha", self.alpha),
+                pretty_str("inv", self.inv),
+            ]
+        )
+
+    def test_matrix_dimensions(self, z=None, H=None, R=None, F=None, Q=None):
+        """
+        Performs a series of asserts to check that the size of everything
+        is what it should be. This can help you debug problems in your design.
+        If you pass in H, R, F, Q those will be used instead of this object's
+        value for those matrices.
+        Testing `z` (the measurement) is problamatic. x is a vector, and can be
+        implemented as either a 1D array or as a nx1 column vector. Thus Hx
+        can be of different shapes. Then, if Hx is a single value, it can
+        be either a 1D array or 2D vector. If either is true, z can reasonably
+        be a scalar (either '3' or np.array('3') are scalars under this
+        definition), a 1D, 1 element array, or a 2D, 1 element array. You are
+        allowed to pass in any combination that works.
+        """
+
+        if H is None:
+            H = self.H
+        if R is None:
+            R = self.R
+        if F is None:
+            F = self.F
+        if Q is None:
+            Q = self.Q
+        x = self.x
+        P = self.P
+
+        assert x.ndim == 1 or x.ndim == 2, "x must have one or two dimensions, but has {}".format(x.ndim)
+
+        if x.ndim == 1:
+            assert x.shape[0] == self.dim_x, "Shape of x must be ({},{}), but is {}".format(self.dim_x, 1, x.shape)
+        else:
+            assert x.shape == (
+                self.dim_x,
+                1,
+            ), "Shape of x must be ({},{}), but is {}".format(self.dim_x, 1, x.shape)
+
+        assert P.shape == (
+            self.dim_x,
+            self.dim_x,
+        ), "Shape of P must be ({},{}), but is {}".format(self.dim_x, self.dim_x, P.shape)
+
+        assert Q.shape == (
+            self.dim_x,
+            self.dim_x,
+        ), "Shape of Q must be ({},{}), but is {}".format(self.dim_x, self.dim_x, P.shape)
+
+        assert F.shape == (
+            self.dim_x,
+            self.dim_x,
+        ), "Shape of F must be ({},{}), but is {}".format(self.dim_x, self.dim_x, F.shape)
+
+        assert np.ndim(H) == 2, "Shape of H must be (dim_z, {}), but is {}".format(P.shape[0], shape(H))
+
+        assert H.shape[1] == P.shape[0], "Shape of H must be (dim_z, {}), but is {}".format(P.shape[0], H.shape)
+
+        # shape of R must be the same as HPH'
+        hph_shape = (H.shape[0], H.shape[0])
+        r_shape = shape(R)
+
+        if H.shape[0] == 1:
+            # r can be scalar, 1D, or 2D in this case
+            assert r_shape in [
+                (),
+                (1,),
+                (1, 1),
+            ], "R must be scalar or one element array, but is shaped {}".format(r_shape)
+        else:
+            assert r_shape == hph_shape, "shape of R should be {} but it is {}".format(hph_shape, r_shape)
+
+        if z is not None:
+            z_shape = shape(z)
+        else:
+            z_shape = (self.dim_z, 1)
+
+        # H@x must have shape of z
+        Hx = dot(H, x)
+
+        if z_shape == ():  # scalar or np.array(scalar)
+            assert Hx.ndim == 1 or shape(Hx) == (
+                1,
+                1,
+            ), "shape of z should be {}, not {} for the given H".format(shape(Hx), z_shape)
+
+        elif shape(Hx) == (1,):
+            assert z_shape[0] == 1, "Shape of z must be {} for the given H".format(shape(Hx))
+
+        else:
+            assert z_shape == shape(Hx) or (
+                len(z_shape) == 1 and shape(Hx) == (z_shape[0], 1)
+            ), "shape of z should be {}, not {} for the given H".format(shape(Hx), z_shape)
+
+        if np.ndim(Hx) > 1 and shape(Hx) != (1, 1):
+            assert shape(Hx) == z_shape, "shape of z should be {} for the given H, but it is {}".format(
+                shape(Hx), z_shape
+            )
+
+
+def update(x, P, z, R, H=None, return_all=False):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    update(1, 2, 1, 1, 1)  # univariate
+    update(x, P, 1
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    P : numpy.array(dim_x, dim_x), or float
+        Covariance matrix
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    R : numpy.array(dim_z, dim_z), or float
+        Measurement noise matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    return_all : bool, default False
+        If true, y, K, S, and log_likelihood are returned, otherwise
+        only x and P are returned.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    P : numpy.array
+        Posterior covariance matrix
+    y : numpy.array or scalar
+        Residua. Difference between measurement and state in measurement space
+    K : numpy.array
+        Kalman gain
+    S : numpy.array
+        System uncertainty in measurement space
+    log_likelihood : float
+        log likelihood of the measurement
+    """
+
+    # pylint: disable=bare-except
+
+    if z is None:
+        if return_all:
+            return x, P, None, None, None, None
+        return x, P
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # project system uncertainty into measurement space
+    S = dot(dot(H, P), H.T) + R
+
+    # map system uncertainty into kalman gain
+    try:
+        K = dot(dot(P, H.T), linalg.inv(S))
+    except:
+        # can't invert a 1D array, annoyingly
+        K = dot(dot(P, H.T), 1.0 / S)
+
+    # predict new x with residual scaled by the kalman gain
+    x = x + dot(K, y)
+
+    # P = (I-KH)P(I-KH)' + KRK'
+    KH = dot(K, H)
+
+    try:
+        I_KH = np.eye(KH.shape[0]) - KH
+    except:
+        I_KH = np.array([1 - KH])
+    P = dot(dot(I_KH, P), I_KH.T) + dot(dot(K, R), K.T)
+
+    if return_all:
+        # compute log likelihood
+        log_likelihood = logpdf(z, dot(H, x), S)
+        return x, P, y, K, S, log_likelihood
+    return x, P
+
+
+def update_steadystate(x, z, K, H=None):
+    """
+    Add a new measurement (z) to the Kalman filter. If z is None, nothing
+    is changed.
+    Parameters
+    ----------
+    x : numpy.array(dim_x, 1), or float
+        State estimate vector
+    z : (dim_z, 1): array_like
+        measurement for this update. z can be a scalar if dim_z is 1,
+        otherwise it must be convertible to a column vector.
+    K : numpy.array, or float
+        Kalman gain matrix
+    H : numpy.array(dim_x, dim_x), or float, optional
+        Measurement function. If not provided, a value of 1 is assumed.
+    Returns
+    -------
+    x : numpy.array
+        Posterior state estimate vector
+    Examples
+    --------
+    This can handle either the multidimensional or unidimensional case. If
+    all parameters are floats instead of arrays the filter will still work,
+    and return floats for x, P as the result.
+    >>> update_steadystate(1, 2, 1)  # univariate
+    >>> update_steadystate(x, P, z, H)
+    """
+
+    if z is None:
+        return x
+
+    if H is None:
+        H = np.array([1])
+
+    if np.isscalar(H):
+        H = np.array([H])
+
+    Hx = np.atleast_1d(dot(H, x))
+    z = reshape_z(z, Hx.shape[0], x.ndim)
+
+    # error (residual) between measurement and prediction
+    y = z - Hx
+
+    # estimate new x with residual scaled by the kalman gain
+    return x + dot(K, y)
+
+
+def predict(x, P, F=1, Q=0, u=0, B=1, alpha=1.0):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    Q : numpy.array, Optional
+        Process noise matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    alpha : float, Optional, default=1.0
+        Fading memory setting. 1.0 gives the normal Kalman filter, and
+        values slightly larger than 1.0 (such as 1.02) give a fading
+        memory effect - previous measurements have less influence on the
+        filter's estimates. This formulation of the Fading memory filter
+        (there are many) is due to Dan Simon
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    P : numpy.array
+        Prior covariance matrix
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+    P = (alpha * alpha) * dot(dot(F, P), F.T) + Q
+
+    return x, P
+
+
+def predict_steadystate(x, F=1, u=0, B=1):
+    """
+    Predict next state (prior) using the Kalman filter state propagation
+    equations. This steady state form only computes x, assuming that the
+    covariance is constant.
+    Parameters
+    ----------
+    x : numpy.array
+        State estimate vector
+    P : numpy.array
+        Covariance matrix
+    F : numpy.array()
+        State Transition matrix
+    u : numpy.array, Optional, default 0.
+        Control vector. If non-zero, it is multiplied by B
+        to create the control input into the system.
+    B : numpy.array, optional, default 0.
+        Control transition matrix.
+    Returns
+    -------
+    x : numpy.array
+        Prior state estimate vector
+    """
+
+    if np.isscalar(F):
+        F = np.array(F)
+    x = dot(F, x) + dot(B, u)
+
+    return x
+
+
+def batch_filter(x, P, zs, Fs, Qs, Hs, Rs, Bs=None, us=None, update_first=False, saver=None):
+    """
+    Batch processes a sequences of measurements.
+    Parameters
+    ----------
+    zs : list-like
+        list of measurements at each time step. Missing measurements must be
+        represented by None.
+    Fs : list-like
+        list of values to use for the state transition matrix matrix.
+    Qs : list-like
+        list of values to use for the process error
+        covariance.
+    Hs : list-like
+        list of values to use for the measurement matrix.
+    Rs : list-like
+        list of values to use for the measurement error
+        covariance.
+    Bs : list-like, optional
+        list of values to use for the control transition matrix;
+        a value of None in any position will cause the filter
+        to use `self.B` for that time step.
+    us : list-like, optional
+        list of values to use for the control input vector;
+        a value of None in any position will cause the filter to use
+        0 for that time step.
+    update_first : bool, optional
+        controls whether the order of operations is update followed by
+        predict, or predict followed by update. Default is predict->update.
+        saver : filterpy.common.Saver, optional
+            filterpy.common.Saver object. If provided, saver.save() will be
+            called after every epoch
+    Returns
+    -------
+    means : np.array((n,dim_x,1))
+        array of the state for each time step after the update. Each entry
+        is an np.array. In other words `means[k,:]` is the state at step
+        `k`.
+    covariance : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the update.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    means_predictions : np.array((n,dim_x,1))
+        array of the state for each time step after the predictions. Each
+        entry is an np.array. In other words `means[k,:]` is the state at
+        step `k`.
+    covariance_predictions : np.array((n,dim_x,dim_x))
+        array of the covariances for each time step after the prediction.
+        In other words `covariance[k,:,:]` is the covariance at step `k`.
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        Fs = [kf.F for t in range (40)]
+        Hs = [kf.H for t in range (40)]
+        (mu, cov, _, _) = kf.batch_filter(zs, Rs=R_list, Fs=Fs, Hs=Hs, Qs=None,
+                                          Bs=None, us=None, update_first=False)
+        (xs, Ps, Ks, Pps) = kf.rts_smoother(mu, cov, Fs=Fs, Qs=None)
+    """
+
+    n = np.size(zs, 0)
+    dim_x = x.shape[0]
+
+    # mean estimates from Kalman Filter
+    if x.ndim == 1:
+        means = zeros((n, dim_x))
+        means_p = zeros((n, dim_x))
+    else:
+        means = zeros((n, dim_x, 1))
+        means_p = zeros((n, dim_x, 1))
+
+    # state covariances from Kalman Filter
+    covariances = zeros((n, dim_x, dim_x))
+    covariances_p = zeros((n, dim_x, dim_x))
+
+    if us is None:
+        us = [0.0] * n
+        Bs = [0.0] * n
+
+    if update_first:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+            if saver is not None:
+                saver.save()
+    else:
+        for i, (z, F, Q, H, R, B, u) in enumerate(zip(zs, Fs, Qs, Hs, Rs, Bs, us)):
+
+            x, P = predict(x, P, u=u, B=B, F=F, Q=Q)
+            means_p[i, :] = x
+            covariances_p[i, :, :] = P
+
+            x, P = update(x, P, z, R=R, H=H)
+            means[i, :] = x
+            covariances[i, :, :] = P
+            if saver is not None:
+                saver.save()
+
+    return (means, covariances, means_p, covariances_p)
+
+
+def rts_smoother(Xs, Ps, Fs, Qs):
+    """
+    Runs the Rauch-Tung-Striebel Kalman smoother on a set of
+    means and covariances computed by a Kalman filter. The usual input
+    would come from the output of `KalmanFilter.batch_filter()`.
+    Parameters
+    ----------
+    Xs : numpy.array
+       array of the means (state variable x) of the output of a Kalman
+       filter.
+    Ps : numpy.array
+        array of the covariances of the output of a kalman filter.
+    Fs : list-like collection of numpy.array
+        State transition matrix of the Kalman filter at each time step.
+    Qs : list-like collection of numpy.array, optional
+        Process noise of the Kalman filter at each time step.
+    Returns
+    -------
+    x : numpy.ndarray
+       smoothed means
+    P : numpy.ndarray
+       smoothed state covariances
+    K : numpy.ndarray
+        smoother gain at each step
+    pP : numpy.ndarray
+       predicted state covariances
+    Examples
+    --------
+    .. code-block:: Python
+        zs = [t + random.randn()*4 for t in range (40)]
+        (mu, cov, _, _) = kalman.batch_filter(zs)
+        (x, P, K, pP) = rts_smoother(mu, cov, kf.F, kf.Q)
+    """
+
+    if len(Xs) != len(Ps):
+        raise ValueError("length of Xs and Ps must be the same")
+
+    n = Xs.shape[0]
+    dim_x = Xs.shape[1]
+
+    # smoother gain
+    K = zeros((n, dim_x, dim_x))
+    x, P, pP = Xs.copy(), Ps.copy(), Ps.copy()
+
+    for k in range(n - 2, -1, -1):
+        pP[k] = dot(dot(Fs[k], P[k]), Fs[k].T) + Qs[k]
+
+        # pylint: disable=bad-whitespace
+        K[k] = dot(dot(P[k], Fs[k].T), linalg.inv(pP[k]))
+        x[k] += dot(K[k], x[k + 1] - dot(Fs[k], x[k]))
+        P[k] += dot(dot(K[k], P[k + 1] - pP[k]), K[k].T)
+
+    return (x, P, K, pP)
diff --git a/trackers/integrated_ocsort_embedding/ocsort.py b/trackers/integrated_ocsort_embedding/ocsort.py
new file mode 100644
index 0000000000000000000000000000000000000000..c20d8f28486326b24fb8399ca878084e444764a6
--- /dev/null
+++ b/trackers/integrated_ocsort_embedding/ocsort.py
@@ -0,0 +1,513 @@
+"""
+    This script is adopted from the SORT script by Alex Bewley alex@bewley.ai
+"""
+from __future__ import print_function
+
+import pdb
+import pickle
+
+import cv2
+
+import numpy as np
+from .association import *
+from .embedding import EmbeddingComputer
+from .cmc import CMCComputer
+
+
+def k_previous_obs(observations, cur_age, k):
+    if len(observations) == 0:
+        return [-1, -1, -1, -1, -1]
+    for i in range(k):
+        dt = k - i
+        if cur_age - dt in observations:
+            return observations[cur_age - dt]
+    max_age = max(observations.keys())
+    return observations[max_age]
+
+
+def convert_bbox_to_z(bbox):
+    """
+    Takes a bounding box in the form [x1,y1,x2,y2] and returns z in the form
+      [x,y,s,r] where x,y is the centre of the box and s is the scale/area and r is
+      the aspect ratio
+    """
+    w = bbox[2] - bbox[0]
+    h = bbox[3] - bbox[1]
+    x = bbox[0] + w / 2.0
+    y = bbox[1] + h / 2.0
+    s = w * h  # scale is just area
+    r = w / float(h + 1e-6)
+    return np.array([x, y, s, r]).reshape((4, 1))
+
+
+def convert_bbox_to_z_new(bbox):
+    w = bbox[2] - bbox[0]
+    h = bbox[3] - bbox[1]
+    x = bbox[0] + w / 2.0
+    y = bbox[1] + h / 2.0
+    return np.array([x, y, w, h]).reshape((4, 1))
+
+
+def convert_x_to_bbox_new(x):
+    x, y, w, h = x.reshape(-1)[:4]
+    return np.array([x - w / 2, y - h / 2, x + w / 2, y + h / 2]).reshape(1, 4)
+
+
+def convert_x_to_bbox(x, score=None):
+    """
+    Takes a bounding box in the centre form [x,y,s,r] and returns it in the form
+      [x1,y1,x2,y2] where x1,y1 is the top left and x2,y2 is the bottom right
+    """
+    w = np.sqrt(x[2] * x[3])
+    h = x[2] / w
+    if score == None:
+        return np.array([x[0] - w / 2.0, x[1] - h / 2.0, x[0] + w / 2.0, x[1] + h / 2.0]).reshape((1, 4))
+    else:
+        return np.array([x[0] - w / 2.0, x[1] - h / 2.0, x[0] + w / 2.0, x[1] + h / 2.0, score]).reshape((1, 5))
+
+
+def speed_direction(bbox1, bbox2):
+    cx1, cy1 = (bbox1[0] + bbox1[2]) / 2.0, (bbox1[1] + bbox1[3]) / 2.0
+    cx2, cy2 = (bbox2[0] + bbox2[2]) / 2.0, (bbox2[1] + bbox2[3]) / 2.0
+    speed = np.array([cy2 - cy1, cx2 - cx1])
+    norm = np.sqrt((cy2 - cy1) ** 2 + (cx2 - cx1) ** 2) + 1e-6
+    return speed / norm
+
+
+def new_kf_process_noise(w, h, p=1 / 20, v=1 / 160):
+    Q = np.diag(
+        (
+            (p * w) ** 2,
+            (p * h) ** 2,
+            (p * w) ** 2,
+            (p * h) ** 2,
+            (v * w) ** 2,
+            (v * h) ** 2,
+            (v * w) ** 2,
+            (v * h) ** 2,
+        )
+    )
+    return Q
+
+
+def new_kf_measurement_noise(w, h, m=1 / 20):
+    w_var = (m * w) ** 2
+    h_var = (m * h) ** 2
+    R = np.diag((w_var, h_var, w_var, h_var))
+    return R
+
+
+class KalmanBoxTracker(object):
+    """
+    This class represents the internal state of individual tracked objects observed as bbox.
+    """
+
+    count = 0
+
+    def __init__(self, bbox, delta_t=3, orig=False, emb=None, alpha=0, new_kf=False):
+        """
+        Initialises a tracker using initial bounding box.
+
+        """
+        # define constant velocity model
+        if not orig:
+            from .kalmanfilter import KalmanFilterNew as KalmanFilter
+        else:
+            from filterpy.kalman import KalmanFilter
+
+        self.new_kf = new_kf
+        if new_kf:
+            self.kf = KalmanFilter(dim_x=8, dim_z=4)
+            self.kf.F = np.array(
+                [
+                    # x y w h x' y' w' h'
+                    [1, 0, 0, 0, 1, 0, 0, 0],
+                    [0, 1, 0, 0, 0, 1, 0, 0],
+                    [0, 0, 1, 0, 0, 0, 1, 0],
+                    [0, 0, 0, 1, 0, 0, 0, 1],
+                    [0, 0, 0, 0, 1, 0, 0, 0],
+                    [0, 0, 0, 0, 0, 1, 0, 0],
+                    [0, 0, 0, 0, 0, 0, 1, 0],
+                    [0, 0, 0, 0, 0, 0, 0, 1],
+                ]
+            )
+            self.kf.H = np.array(
+                [
+                    [1, 0, 0, 0, 0, 0, 0, 0],
+                    [0, 1, 0, 0, 0, 0, 0, 0],
+                    [0, 0, 1, 0, 0, 0, 0, 0],
+                    [0, 0, 0, 1, 0, 0, 0, 0],
+                ]
+            )
+            _, _, w, h = convert_bbox_to_z_new(bbox).reshape(-1)
+            self.kf.P = new_kf_process_noise(w, h)
+            self.kf.P[:4, :4] *= 4
+            self.kf.P[4:, 4:] *= 100
+            # Process and measurement uncertainty happen in functions
+            self.bbox_to_z_func = convert_bbox_to_z_new
+            self.x_to_bbox_func = convert_x_to_bbox_new
+        else:
+            self.kf = KalmanFilter(dim_x=7, dim_z=4)
+            self.kf.F = np.array(
+                [
+                    # x  y  s  r  x' y' s'
+                    [1, 0, 0, 0, 1, 0, 0],
+                    [0, 1, 0, 0, 0, 1, 0],
+                    [0, 0, 1, 0, 0, 0, 1],
+                    [0, 0, 0, 1, 0, 0, 0],
+                    [0, 0, 0, 0, 1, 0, 0],
+                    [0, 0, 0, 0, 0, 1, 0],
+                    [0, 0, 0, 0, 0, 0, 1],
+                ]
+            )
+            self.kf.H = np.array(
+                [
+                    [1, 0, 0, 0, 0, 0, 0],
+                    [0, 1, 0, 0, 0, 0, 0],
+                    [0, 0, 1, 0, 0, 0, 0],
+                    [0, 0, 0, 1, 0, 0, 0],
+                ]
+            )
+            self.kf.R[2:, 2:] *= 10.0
+            self.kf.P[4:, 4:] *= 1000.0  # give high uncertainty to the unobservable initial velocities
+            self.kf.P *= 10.0
+            self.kf.Q[-1, -1] *= 0.01
+            self.kf.Q[4:, 4:] *= 0.01
+            self.bbox_to_z_func = convert_bbox_to_z
+            self.x_to_bbox_func = convert_x_to_bbox
+
+            # Attempt
+            # self.kf.P[2, 2] = 10000
+            # self.kf.R[2, 2] = 10000
+
+        self.kf.x[:4] = self.bbox_to_z_func(bbox)
+
+        self.time_since_update = 0
+        self.id = KalmanBoxTracker.count
+        KalmanBoxTracker.count += 1
+        self.history = []
+        self.hits = 0
+        self.hit_streak = 0
+        self.age = 0
+        """
+        NOTE: [-1,-1,-1,-1,-1] is a compromising placeholder for non-observation status, the same for the return of 
+        function k_previous_obs. It is ugly and I do not like it. But to support generate observation array in a 
+        fast and unified way, which you would see below k_observations = np.array([k_previous_obs(...]]), let's bear it for now.
+        """
+        # Used for OCR
+        self.last_observation = np.array([-1, -1, -1, -1, -1])  # placeholder
+        # Used to output track after min_hits reached
+        self.history_observations = []
+        # Used for velocity
+        self.observations = dict()
+        self.velocity = None
+        self.delta_t = delta_t
+
+        self.emb = emb
+
+        self.frozen = False
+
+    def update(self, bbox):
+        """
+        Updates the state vector with observed bbox.
+        """
+        if bbox is not None:
+            self.frozen = False
+
+            if self.last_observation.sum() >= 0:  # no previous observation
+                previous_box = None
+                for dt in range(self.delta_t, 0, -1):
+                    if self.age - dt in self.observations:
+                        previous_box = self.observations[self.age - dt]
+                        break
+                if previous_box is None:
+                    previous_box = self.last_observation
+                """
+                  Estimate the track speed direction with observations \Delta t steps away
+                """
+                self.velocity = speed_direction(previous_box, bbox)
+            """
+              Insert new observations. This is a ugly way to maintain both self.observations
+              and self.history_observations. Bear it for the moment.
+            """
+            self.last_observation = bbox
+            self.observations[self.age] = bbox
+            self.history_observations.append(bbox)
+
+            self.time_since_update = 0
+            self.history = []
+            self.hits += 1
+            self.hit_streak += 1
+            if self.new_kf:
+                R = new_kf_measurement_noise(self.kf.x[2, 0], self.kf.x[3, 0])
+                self.kf.update(self.bbox_to_z_func(bbox), R=R, new_kf=True)
+            else:
+                self.kf.update(self.bbox_to_z_func(bbox))
+        else:
+            self.kf.update(bbox, new_kf=self.new_kf)
+            self.frozen = True
+
+    def update_emb(self, emb, alpha=0.9):
+        self.emb = alpha * self.emb + (1 - alpha) * emb
+        self.emb /= np.linalg.norm(self.emb)
+
+    def get_emb(self):
+        return self.emb
+
+    def apply_affine_correction(self, affine):
+        m = affine[:, :2]
+        t = affine[:, 2].reshape(2, 1)
+        # For OCR
+        if self.last_observation.sum() > 0:
+            ps = self.last_observation[:4].reshape(2, 2).T
+            ps = m @ ps + t
+            self.last_observation[:4] = ps.T.reshape(-1)
+
+        # Apply to each box in the range of velocity computation
+        for dt in range(self.delta_t, -1, -1):
+            if self.age - dt in self.observations:
+                ps = self.observations[self.age - dt][:4].reshape(2, 2).T
+                ps = m @ ps + t
+                self.observations[self.age - dt][:4] = ps.T.reshape(-1)
+
+        # Also need to change kf state, but might be frozen
+        self.kf.apply_affine_correction(m, t, self.new_kf)
+
+    def predict(self):
+        """
+        Advances the state vector and returns the predicted bounding box estimate.
+        """
+        # Don't allow negative bounding boxes
+        if self.new_kf:
+            if self.kf.x[2] + self.kf.x[6] <= 0:
+                self.kf.x[6] = 0
+            if self.kf.x[3] + self.kf.x[7] <= 0:
+                self.kf.x[7] = 0
+
+            # Stop velocity, will update in kf during OOS
+            if self.frozen:
+                self.kf.x[6] = self.kf.x[7] = 0
+            Q = new_kf_process_noise(self.kf.x[2, 0], self.kf.x[3, 0])
+        else:
+            if (self.kf.x[6] + self.kf.x[2]) <= 0:
+                self.kf.x[6] *= 0.0
+            Q = None
+
+        self.kf.predict(Q=Q)
+        self.age += 1
+        if self.time_since_update > 0:
+            self.hit_streak = 0
+        self.time_since_update += 1
+        self.history.append(self.x_to_bbox_func(self.kf.x))
+        return self.history[-1]
+
+    def get_state(self):
+        """
+        Returns the current bounding box estimate.
+        """
+        return self.x_to_bbox_func(self.kf.x)
+
+    def mahalanobis(self, bbox):
+        """Should be run after a predict() call for accuracy."""
+        return self.kf.md_for_measurement(self.bbox_to_z_func(bbox))
+
+
+"""
+    We support multiple ways for association cost calculation, by default
+    we use IoU. GIoU may have better performance in some situations. We note 
+    that we hardly normalize the cost by all methods to (0,1) which may not be 
+    the best practice.
+"""
+ASSO_FUNCS = {
+    "iou": iou_batch,
+    "giou": giou_batch,
+    "ciou": ciou_batch,
+    "diou": diou_batch,
+    "ct_dist": ct_dist,
+}
+
+
+class Track:
+    def __init__(self, track_id, tlrb, score):
+        self.track_id = track_id
+        self.tlwh = [tlrb[0], tlrb[1], tlrb[2] - tlrb[0], tlrb[3] - tlrb[1]]
+        self.score = score
+
+
+class OCSort(object):
+    def __init__(
+        self,
+        det_thresh,
+        max_age=30,
+        min_hits=3,
+        iou_threshold=0.3,
+        delta_t=3,
+        asso_func="iou",
+        inertia=0.2,
+        w_association_emb=0.75,
+        alpha_fixed_emb=0.95,
+        aw_param=0.5,
+        embedding_off=False,
+        cmc_off=True,
+        aw_off=False,
+        new_kf_off=False,
+        grid_off=False,
+        **kwargs,
+    ):
+        """
+        Sets key parameters for SORT
+        """
+        self.max_age = max_age
+        self.min_hits = min_hits
+        self.iou_threshold = iou_threshold
+        self.trackers = []
+        self.frame_count = 0
+        self.det_thresh = det_thresh
+        self.delta_t = delta_t
+        self.asso_func = ASSO_FUNCS[asso_func]
+        self.inertia = inertia
+        self.w_association_emb = w_association_emb
+        self.alpha_fixed_emb = alpha_fixed_emb
+        self.aw_param = aw_param
+        KalmanBoxTracker.count = 0
+
+        # self.embedder = EmbeddingComputer(kwargs["args"].dataset, kwargs["args"].test_dataset, grid_off)
+        # self.cmc = CMCComputer()
+        self.embedding_off = embedding_off
+        self.cmc_off = cmc_off
+        self.aw_off = aw_off
+        self.new_kf_off = new_kf_off
+        self.grid_off = grid_off
+
+    def update(self, fdets, img):
+        """
+        Params:
+          dets - a numpy array of detections in the format [[x1,y1,x2,y2,score],[x1,y1,x2,y2,score],...]
+        Requires: this method must be called once for each frame even with empty detections (use np.empty((0, 5)) for frames without detections).
+        Returns the a similar array, where the last column is the object ID.
+        NOTE: The number of objects returned may differ from the number of detections provided.
+        """
+        #####
+        remain_inds = fdets[:, 4] > self.det_thresh
+        dets, dets_embs = fdets[remain_inds, 0:5], fdets[remain_inds, 5:]
+        self.frame_count += 1
+
+        # CMC
+        if not self.cmc_off:
+            transform = self.cmc.compute_affine(img_numpy, dets[:, :4], tag)
+            for trk in self.trackers:
+                trk.apply_affine_correction(transform)
+
+        trust = (dets[:, 4] - self.det_thresh) / (1 - self.det_thresh)
+        af = self.alpha_fixed_emb
+        # From [self.alpha_fixed_emb, 1], goes to 1 as detector is less confident
+        dets_alpha = af + (1 - af) * (1 - trust)
+
+        # get predicted locations from existing trackers.
+        trks = np.zeros((len(self.trackers), 5))
+        trk_embs = []
+        to_del = []
+        ret = []
+        for t, trk in enumerate(trks):
+            pos = self.trackers[t].predict()[0]
+            trk[:] = [pos[0], pos[1], pos[2], pos[3], 0]
+            if np.any(np.isnan(pos)):
+                to_del.append(t)
+            else:
+                trk_embs.append(self.trackers[t].get_emb())
+        trks = np.ma.compress_rows(np.ma.masked_invalid(trks))
+        # Shape = (num_trackers, 3, 512) if grid
+        trk_embs = np.array(trk_embs)
+        for t in reversed(to_del):
+            self.trackers.pop(t)
+
+        velocities = np.array([trk.velocity if trk.velocity is not None else np.array((0, 0)) for trk in self.trackers])
+        last_boxes = np.array([trk.last_observation for trk in self.trackers])
+        k_observations = np.array([k_previous_obs(trk.observations, trk.age, self.delta_t) for trk in self.trackers])
+
+        """
+            First round of association
+        """
+        matched, unmatched_dets, unmatched_trks = associate(
+            dets,
+            trks,
+            dets_embs,
+            trk_embs,
+            self.iou_threshold,
+            velocities,
+            k_observations,
+            self.inertia,
+            self.w_association_emb,
+            self.aw_off,
+            self.aw_param,
+            self.embedding_off,
+            self.grid_off,
+        )
+        for m in matched:
+            self.trackers[m[1]].update(dets[m[0], :])
+            self.trackers[m[1]].update_emb(dets_embs[m[0]], alpha=dets_alpha[m[0]])
+        """
+            Second round of associaton by OCR
+        """
+        if unmatched_dets.shape[0] > 0 and unmatched_trks.shape[0] > 0:
+            left_dets = dets[unmatched_dets]
+            left_dets_embs = dets_embs[unmatched_dets]
+            left_trks = last_boxes[unmatched_trks]
+            left_trks_embs = trk_embs[unmatched_trks]
+
+            # TODO: maybe use embeddings here
+            iou_left = self.asso_func(left_dets, left_trks)
+            iou_left = np.array(iou_left)
+            if iou_left.max() > self.iou_threshold:
+                """
+                NOTE: by using a lower threshold, e.g., self.iou_threshold - 0.1, you may
+                get a higher performance especially on MOT17/MOT20 datasets. But we keep it
+                uniform here for simplicity
+                """
+                rematched_indices = linear_assignment(-iou_left)
+
+                to_remove_det_indices = []
+                to_remove_trk_indices = []
+                for m in rematched_indices:
+                    det_ind, trk_ind = unmatched_dets[m[0]], unmatched_trks[m[1]]
+                    if iou_left[m[0], m[1]] < self.iou_threshold:
+                        continue
+                    self.trackers[trk_ind].update(dets[det_ind, :])
+                    self.trackers[trk_ind].update_emb(dets_embs[det_ind], alpha=dets_alpha[det_ind])
+                    to_remove_det_indices.append(det_ind)
+                    to_remove_trk_indices.append(trk_ind)
+                unmatched_dets = np.setdiff1d(unmatched_dets, np.array(to_remove_det_indices))
+                unmatched_trks = np.setdiff1d(unmatched_trks, np.array(to_remove_trk_indices))
+
+        for m in unmatched_trks:
+            self.trackers[m].update(None)
+
+        # create and initialise new trackers for unmatched detections
+        for i in unmatched_dets:
+            trk = KalmanBoxTracker(
+                dets[i, :], delta_t=self.delta_t, emb=dets_embs[i], alpha=dets_alpha[i], new_kf=not self.new_kf_off
+            )
+            self.trackers.append(trk)
+        i = len(self.trackers)
+        for trk in reversed(self.trackers):
+            if trk.last_observation.sum() < 0:
+                d = trk.get_state()[0]
+            else:
+                """
+                this is optional to use the recent observation or the kalman filter prediction,
+                we didn't notice significant difference here
+                """
+                d = trk.last_observation[:4]
+            if (trk.time_since_update < 1) and (trk.hit_streak >= self.min_hits or self.frame_count <= self.min_hits):
+                # +1 as MOT benchmark requires positive
+                # ret.append(np.concatenate((d, [trk.id + 1])).reshape(1, -1))
+                ret.append(Track(trk.id + 1, d, 1))
+            i -= 1
+            # remove dead tracklet
+            if trk.time_since_update > self.max_age:
+                self.trackers.pop(i)
+        return ret
+
+    def dump_cache(self):
+        self.cmc.dump_cache()
+        self.embedder.dump_cache()
diff --git a/trackers/joint_lmb/compute_pd.fis b/trackers/joint_lmb/compute_pd.fis
new file mode 100644
index 0000000000000000000000000000000000000000..9909a9064e3413e5cedd41740b081eca81866d5b
--- /dev/null
+++ b/trackers/joint_lmb/compute_pd.fis
@@ -0,0 +1,47 @@
+[System]
+Name='compute_pd'
+Type='mamdani'
+Version=2.0
+NumInputs=2
+NumOutputs=1
+NumRules=9
+AndMethod='min'
+OrMethod='max'
+ImpMethod='min'
+AggMethod='max'
+DefuzzMethod='centroid'
+
+[Input1]
+Name='AreaRate'
+Range=[0 2]
+NumMFs=3
+MF1='L':'trimf',[0 0 0.6]
+MF2='M':'trimf',[0 1 2]
+MF3='H':'trimf',[1.4 2 2]
+
+[Input2]
+Name='IOA'
+Range=[0 1]
+NumMFs=3
+MF1='L':'trimf',[0 0 0.3]
+MF2='M':'trimf',[0 0.5 1]
+MF3='H':'trimf',[0.7 1 1]
+
+[Output1]
+Name='PD'
+Range=[0.4 0.99]
+NumMFs=3
+MF1='L':'trimf',[0.4 0.4 0.577]
+MF2='M':'trimf',[0.4 0.695 0.99]
+MF3='H':'trimf',[0.813 0.99 0.99]
+
+[Rules]
+1 1, 2 (1) : 1
+2 1, 2 (1) : 1
+3 1, 3 (1) : 1
+1 2, 1 (1) : 1
+2 2, 2 (1) : 1
+3 2, 3 (1) : 1
+1 3, 1 (1) : 1
+2 3, 1 (1) : 1
+3 3, 1 (1) : 1
diff --git a/trackers/joint_lmb/joint_lmb.py b/trackers/joint_lmb/joint_lmb.py
new file mode 100644
index 0000000000000000000000000000000000000000..c9d1338847f23ed95b06478c0278f4dfc5dc78a4
--- /dev/null
+++ b/trackers/joint_lmb/joint_lmb.py
@@ -0,0 +1,507 @@
+from scipy.spatial.distance import cdist
+from scipy.stats.distributions import chi2
+from scipy.special import logsumexp
+import numpy as np
+import lap
+
+from .utils import gate_meas_gms_idx, kalman_update_multiple, esf
+from cpputils import bboxes_ioi_xyah_back2front, ComputePD, Murty, esf, bbox_iou_xyah, bboxes_ioi_xyah_back2front_all
+
+
+class Track:
+    def __init__(self, track_id, tlrb, score):
+        self.track_id = track_id
+        self.tlwh = [tlrb[0], tlrb[1], tlrb[2] - tlrb[0], tlrb[3] - tlrb[1]]
+        self.score = score
+
+
+class ModelParas:
+    # filter parameters
+    def __init__(self):
+        self.T_max = 100  # maximum number of tracks
+        self.track_threshold = 1e-3  # threshold to prune tracks
+        self.H_upd = 500  # requested number of updated components/hypotheses (for GLMB update)
+
+        self.x_dim = 8
+        self.z_dim = 4
+        self.P_G = 0.99  # gate size in percentage
+        self.gamma = chi2.ppf(self.P_G, self.z_dim)  # inv chi^2 dn gamma value
+        self.P_D = .8  # probability of detection in measurements
+        self.P_S = .99  # survival/death parameters
+
+        # clutter parameters
+        self.lambda_c = 0.5  # poisson average rate of uniform clutter (per scan)
+        self.range_c = np.array([[0, 1920], [0, 1080]])  # uniform clutter region
+        self.pdf_c = 1 / np.prod(self.range_c[:, 1] - self.range_c[:, 0])  # uniform clutter density
+        self.model_c = self.lambda_c * self.pdf_c
+
+        float_precision = 'f8'
+        # observation noise covariance
+        self.R = np.array([[50., 0., 0., 0.],
+                           [0., 50., 0., 0.],
+                           [0., 0., 0.01, 0.],
+                           [0., 0., 0., 50.]], dtype=float_precision)
+        T = 1  # sate vector [x,y,a,h,dx,dy,da,dh]
+        sigma_xy, sigma_a, sigma_h = 3 ** 2, 1e-4, 3 ** 2
+        self.Q = np.array(
+            [[T ** 4 * (sigma_xy / 4), 0, 0, 0, T ** 3 * (sigma_xy / 2), 0, 0, 0],  # process noise covariance
+             [0, T ** 4 * (sigma_xy / 4), 0, 0, 0, T ** 3 * (sigma_xy / 2), 0, 0],
+             [0, 0, T ** 4 * (sigma_a / 4), 0, 0, 0, T ** 3 * (sigma_a / 2), 0],
+             [0, 0, 0, T ** 4 * (sigma_h / 4), 0, 0, 0, T ** 3 * (sigma_h / 2)],
+             [T ** 3 * (sigma_xy / 2), 0, 0, 0, sigma_xy * T ** 2, 0, 0, 0],
+             [0, T ** 3 * (sigma_xy / 2), 0, 0, 0, sigma_xy * T ** 2, 0, 0],
+             [0, 0, T ** 3 * (sigma_a / 2), 0, 0, 0, sigma_a * T ** 2, 0],
+             [0, 0, 0, T ** 3 * (sigma_h / 2), 0, 0, 0, sigma_h * T ** 2]], dtype=float_precision)
+
+        self.F = np.array([[1, 0, 0, 0, 1, 0, 0, 0],  # Motion model: state transition matrix
+                           [0, 1, 0, 0, 0, 1, 0, 0],
+                           [0, 0, 1, 0, 0, 0, 1, 0],
+                           [0, 0, 0, 1, 0, 0, 0, 1],
+                           [0, 0, 0, 0, 1, 0, 0, 0],
+                           [0, 0, 0, 0, 0, 1, 0, 0],
+                           [0, 0, 0, 0, 0, 0, 1, 0],
+                           [0, 0, 0, 0, 0, 0, 0, 1]], dtype=float_precision)
+        self.H = np.array([[1, 0, 0, 0, 0, 0, 0, 0],  # observation matrix
+                           [0, 1, 0, 0, 0, 0, 0, 0],
+                           [0, 0, 1, 0, 0, 0, 0, 0],
+                           [0, 0, 0, 1, 0, 0, 0, 0]], dtype=float_precision)
+        # Use P_birth from width, height of detected bbox diag(w, h, w, h)
+        self.b_thresh = 0.95  # only birth a new target at a measurement that has lower assign_prob than this threshold
+        self.lambda_b = 0.1  # Set lambda_b to the mean cardinality of the birth multi-Bernoulli RFS
+        self.prob_birth = 0.03  # Initial existence probability of a birth track
+    # END
+
+
+class Target:
+    # track table for GLMB (cell array of structs for individual tracks)
+    # (1) r: existence probability
+    # (2) Gaussian Mixture w (weight), m (mean), P (covariance matrix)
+    # (3) Label: birth time & index of target at birth time step
+    # (4) gatemeas: indexes gating measurement (using  Chi-squared distribution)
+    # (5) deep feature: representing feature information extracted from re-identification network
+    def __init__(self, z, feat, prob_birth, label, use_feat=True):
+        x_dim = 8
+        max_cpmt = 1000
+
+        # wg, mg, Pg, ..., store temporary Gaussian mixtures while updating, see 'update_gms'
+        self.wg = np.zeros(max_cpmt, dtype='f8')
+        self.mg = np.zeros((x_dim, max_cpmt), dtype='f8')
+        self.Pg = np.zeros((x_dim, x_dim, max_cpmt), dtype='f8')
+        self.idxg = 0
+        # store number of Gaussian mixtures before updating, see 'update_gms'
+        self.gm_len = 0
+
+        self.m = np.r_[z, np.zeros_like(z)][:, np.newaxis]
+        wh2 = (z[3] + z[2] * z[3]) / 2  # half perimeter
+        self.P = np.diag([wh2, wh2, 1, wh2, wh2, wh2, 1, wh2])[:, :, np.newaxis]
+        self.alpha_feat = 0.9
+        self.r = prob_birth  # existence probability of this birth
+        self.w = np.ones(1)  # weights of Gaussians for birth track
+        self.l = label  # label of this track
+        self.r_max = 0  # maximum existence probability, use for hysteresis
+        self.last_active = 0  # last frame, this track is not pruned or death
+        self.use_feat = use_feat  # True/False whether using re-identification feature or NOT
+        self.feat = None
+        if use_feat:
+            self.feat = feat
+        self.gatemeas = np.empty(0, dtype=int)
+
+    def predict_gms(self, model):
+        self.r = model.P_S * self.r
+
+        plength = self.m.shape[1]
+        m_predict = np.zeros(self.m.shape)
+        P_predict = np.zeros(self.P.shape)
+        for idxp in range(plength):
+            m_temp = np.dot(model.F, self.m[:, idxp])
+            P_temp = model.Q + np.dot(model.F, np.dot(self.P[:, :, idxp], model.F.T))
+            m_predict[:, idxp] = m_temp
+            P_predict[:, :, idxp] = P_temp
+
+        self.m = m_predict
+        self.P = P_predict
+
+    def update_gms(self, model, z, feat):
+        #  =========== gating by tracks ===========
+        zlength, plength = z.shape[0], self.m.shape[1]
+        if zlength == 0:
+            self.gatemeas = np.empty(0)
+        else:
+            valid_idx = np.zeros(zlength, dtype=bool)
+            for j in range(plength):
+                Sj = model.R + np.dot(np.dot(model.H, self.P[:, :, j]), model.H.T)
+                Vs = np.linalg.cholesky(Sj)
+                inv_sqrt_Sj = np.linalg.inv(Vs)
+                nu = z.T - np.tile(np.dot(model.H, self.m[:, j].reshape(-1, 1)), zlength)
+                dist = sum(np.square(np.dot(inv_sqrt_Sj, nu)))
+                valid_idx = np.logical_or(valid_idx, dist < model.gamma)
+            if self.use_feat:
+                cdist_tmp = cdist(feat, self.feat[np.newaxis, :], metric='cosine').flatten()
+                self.gatemeas = np.nonzero(np.logical_or(valid_idx, cdist_tmp < 0.3))[0]
+                dist = cdist(self.feat[np.newaxis, :], feat[self.gatemeas])[0]
+            else:
+                self.gatemeas = np.nonzero(valid_idx)[0]
+                dist = np.ones(len(self.gatemeas))
+        #  ========================================
+
+        self.idxg = 0
+        # Gaussian mixtures for misdetection
+        length = len(self.w)
+        self.wg[:length] = self.w
+        self.mg[:, :length] = self.m
+        self.Pg[:, :, :length] = self.P
+        self.idxg += length
+        self.gm_len = length
+
+        # Kalman update for each Gaussian with each gating measurement
+        cost_update = np.zeros(len(self.gatemeas))
+        for i, emm in enumerate(self.gatemeas):
+            qz_temp, m_temp, P_temp = kalman_update_multiple(z[emm], model, self.m, self.P)
+            w_temp = np.multiply(qz_temp, self.w) + np.spacing(1)
+
+            pm_temp = 0.1 * dist[i] ** 14 + 0.9 * (2 - dist[i]) ** 14
+
+            cost_update[i] = sum(w_temp) * pm_temp
+            length = len(qz_temp)
+            self.wg[self.idxg:self.idxg + length] = w_temp / sum(w_temp)
+            self.mg[:, self.idxg:self.idxg + length] = m_temp
+            self.Pg[:, :, self.idxg:self.idxg + length] = P_temp
+            self.idxg += length
+
+        # Copy values back to each fields
+        self.w = self.wg[:self.idxg]
+        self.m = self.mg[:, :self.idxg]
+        self.P = self.Pg[:, :, :self.idxg]
+
+        return cost_update
+
+    # remove Gaussian mixtures in 'update_gm' that are not in ranked assignment
+    def select_gms(self, select_idxs):
+        self.w = self.wg[select_idxs]
+        self.m = self.mg[:, select_idxs]
+        self.P = self.Pg[:, :, select_idxs]
+
+    def finalize_glmb2lmb(self, sums, association_idx, feat, time_step):
+        if association_idx > 0:  # association_idx = 0, misdetection, keeping the same feature
+            if self.use_feat:
+                self.feat = self.alpha_feat * self.feat
+                self.feat += (1 - self.alpha_feat) * feat[int(association_idx - 1), :]
+                self.feat /= np.linalg.norm(self.feat)
+            self.last_active = time_step  # only update if the highest hypothesis weight is not miss-detection
+        repeat_sums = np.repeat(sums, self.gm_len)
+        self.w *= repeat_sums
+        self.r = sum(self.w)
+        if self.r_max < self.r:
+            self.r_max = self.r
+        self.w = self.w / self.r
+
+    def re_activate(self, z, feat, prob_birth):
+        self.m = np.r_[z, np.zeros_like(z)][:, np.newaxis]
+        wh2 = (z[3] + z[2] * z[3]) / 2
+        self.P = np.diag([wh2, wh2, 1, wh2, wh2, wh2, 1, wh2])[:, :, np.newaxis]
+        self.r = prob_birth
+        self.w = np.ones(1)
+        self.feat = feat
+
+    def cleanup(self, elim_threshold=1e-5, l_max=10):
+        # Gaussian prune, remove components that have weight lower than a threshold
+        idx = np.nonzero(self.w > elim_threshold)[0]
+        self.w = self.w[idx]
+        self.m = self.m[:, idx]
+        self.P = self.P[:, :, idx]
+        # Gaussian cap, limit on number of Gaussians in each track
+        if len(self.w) > l_max:
+            idx = np.argsort(-self.w)
+            w_new = self.w[idx[:l_max]]
+            self.w = w_new * (sum(self.w) / sum(w_new))
+            self.m = self.m[:, idx[:l_max]]
+            self.P = self.P[:, :, idx[:l_max]]
+
+
+class LMB:
+    def __init__(self, track_thresh, use_feat=True):
+        # initial prior
+        self.tt_lmb = []
+        self.tt_birth = []
+        self.glmb_update_w = np.array([1])  # 2, vector of GLMB component/hypothesis weights
+        self.assign_prob = None
+        self.model = ModelParas()
+        self.prune_tracks = []
+        self.X = np.array([])
+        self.L = np.array([], dtype=object)
+        self.tt_lmb_xyah = np.array([])  # LMB tracks state [x,y,a,h]
+        self.tt_lmb_feat = np.array([])  # LMB tracks reid feature
+        self.pd = ComputePD('./trackers/joint_lmb/compute_pd.fis')
+        self.sampling = Murty()
+        self.id = 0
+        self.average_area = 1
+        self.use_feat = use_feat
+        self.frame = 0
+        self.track_thresh = track_thresh
+
+    def jointlmbpredictupdate(self, model, z, feat, k):
+        #  generate birth tracks
+        if k == 0:
+            for idx in range(z.shape[0]):
+                target = Target(z[idx], feat[idx], model.prob_birth, self.id, self.use_feat)
+                self.id += 1  # or label = '0.' + str(idx)
+                self.tt_birth.append(target)
+            self.average_area = sum(z[:, 2] * z[:, 3] ** 2) / z.shape[0]
+
+        # generate surviving tracks
+        for target in self.tt_lmb:
+            target.predict_gms(model)
+        m = z.shape[0]  # number of measurements
+        if m == 0:  # see MOT16-12, frame #445
+            return  # no measurement to update, only predict existing tracks
+
+        # create predicted tracks - concatenation of birth and survival
+        self.tt_lmb += self.tt_birth  # copy track table back to GLMB struct
+        ntracks = len(self.tt_lmb)
+        self.tt_lmb_xyah = np.ascontiguousarray([tt.m[:4, np.argmax(tt.w)] for tt in self.tt_lmb], dtype=np.dtype('f8'))
+
+        # compute Intersection Over Itself (between tt_lmb and estimated tracks) to find P_D for each track
+        avps = np.zeros((ntracks, 1))
+        avpd = np.zeros((ntracks, 1))
+        # object stands close to a camera has a higher bottom coordinate [(0, 0) : (top, left)]
+        # back to front: objects from far to near a camera
+        tt_labels = np.array([tt.l for tt in self.tt_lmb], dtype=np.dtype('int'))
+        mutual_ioi = bboxes_ioi_xyah_back2front(self.tt_lmb_xyah, tt_labels, self.X.T, self.L)
+        self.tt_lmb_xyah[:, 2] = np.clip(self.tt_lmb_xyah[:, 2], 0.15, None)  # constraint 'a' not to be negative
+        area_all = self.tt_lmb_xyah[:, 2] * self.tt_lmb_xyah[:, 3] ** 2
+        area_rate = np.clip(area_all / self.average_area, 0, 2)
+        for tabidx, tabidx_ioa in enumerate(mutual_ioi):
+            # average detection/missed probabilities
+            avpd[tabidx] = self.pd.compute(area_rate[tabidx], tabidx_ioa)
+            # average survival/death probabilities
+            avps[tabidx] = self.tt_lmb[tabidx].r
+        avqd = 1 - avpd
+        avqs = 1 - avps
+
+        # create updated tracks (single target Bayes update)
+        allcostm = np.zeros((ntracks, m))
+        for tabidx in range(ntracks):
+            cost_update = self.tt_lmb[tabidx].update_gms(model, z, feat)
+            allcostm[tabidx, self.tt_lmb[tabidx].gatemeas] = cost_update
+
+        # joint cost matrix, eta_j eq (22) "An Efficient Implementation of the GLMB"
+        eta_j = np.multiply(np.multiply(avps, avpd), allcostm) / model.model_c
+        jointcostm = np.zeros((ntracks, 2 * ntracks + m))
+        np.fill_diagonal(jointcostm, avqs)
+        np.fill_diagonal(jointcostm[:, ntracks:], np.multiply(avps, avqd))
+        jointcostm[:, 2 * ntracks:2 * ntracks + m] = eta_j
+
+        # calculate best updated hypotheses/components
+        # murty's algo/gibbs sampling to calculate m-best assignment hypotheses/components
+        if jointcostm.shape[0] > 0:
+            uasses, nlcost = self.sampling.draw_solutions(-np.log(jointcostm), model.H_upd)
+        else:
+            # no need sampling for empty cost matrix
+            uasses, nlcost = np.empty(0), np.empty(0)
+        uasses = uasses + 1
+        uasses[uasses <= ntracks] = -np.inf  # set not born/track deaths to -inf assignment
+        uasses[(uasses > ntracks) & (uasses <= 2 * ntracks)] = 0  # set survived+missed to 0 assignment
+        # set survived+detected to assignment of measurement index from 1:|Z|
+        uasses[uasses > 2 * ntracks] = uasses[uasses > 2 * ntracks] - 2 * ntracks
+
+        # component updates
+        glmb_nextupdate_w = np.zeros(len(nlcost))
+        self.assign_prob = np.zeros(m)  # adaptive birth weight for each measurement
+        assign_meas = np.zeros((m, len(nlcost)), dtype=int)  # store indexes of measurement assigned to a track
+
+        iois = bboxes_ioi_xyah_back2front_all(self.tt_lmb_xyah)
+        self.pd.set_recompute_cost(avqs, avps, allcostm, model.model_c)
+        # generate corrresponding jointly predicted/updated hypotheses/components
+        for hidx in range(0, len(nlcost)):
+            update_hypcmp_tmp = uasses[hidx, :]
+            new_cost = self.pd.recompute_cost(update_hypcmp_tmp, iois, area_all)
+            # hypothesis/component weight
+            # Vo Ba-Ngu "An efficient implementation of the generalized labeled multi-Bernoulli filter." eq (20)
+            omega_z = -model.lambda_c + m * np.log(model.model_c) - new_cost  # nlcost[hidx]
+            # Get measurement index from uasses (make sure minus 1 from [mindices+1])
+            meas_idx = update_hypcmp_tmp[update_hypcmp_tmp > 0].astype(int) - 1
+            assign_meas[meas_idx, hidx] = 1
+            glmb_nextupdate_w[hidx] = omega_z
+
+        glmb_nextupdate_w = np.exp(glmb_nextupdate_w - logsumexp(glmb_nextupdate_w))  # normalize weights
+
+        self.assign_prob = assign_meas @ glmb_nextupdate_w
+
+        # The following implementation is optimized for GLMB to LMB (glmb2lmb)
+        # Refer "The Labeled Multi-Bernoulli Filter, 2014"
+        for (i, target) in enumerate(self.tt_lmb):
+            notinf_uasses_idxs = np.nonzero(uasses[:, i] >= 0)[0]
+            workon_uasses = uasses[notinf_uasses_idxs, i]
+            workon_weights = glmb_nextupdate_w[notinf_uasses_idxs]
+
+            u, inv = np.unique(workon_uasses, return_inverse=True)
+            if len(u) == 0:  # no measurement association (including misdetection)
+                continue
+            sums = np.zeros(len(u), dtype=workon_weights.dtype)
+            np.add.at(sums, inv, workon_weights)
+
+            # select gating measurement indexes appear in ranked assignment (u: variable)
+            # 0 for mis detection, 1->n for measurement index
+            _, select_idxs, _ = np.intersect1d(np.insert(target.gatemeas + 1, 0, 0), u, return_indices=True)
+
+            # select 'block of gaussian mixtures' that are in 'select_idxs'
+            l_range = np.tile(np.arange(target.gm_len), len(select_idxs))
+            start_idx = np.repeat(select_idxs, target.gm_len) * target.gm_len
+            select_idxs = l_range + start_idx
+            target.select_gms(select_idxs)
+
+            target.finalize_glmb2lmb(sums, u[np.argmax(sums)], feat, time_step=k)
+
+        # create birth tracks
+        self.apdative_birth(self.assign_prob, z, feat, model, k)
+
+    def re_activate_tracks(self, z, feat, model, prob_birth):
+        if not self.use_feat:
+            return False
+        if len(self.prune_tracks) > 0:
+            track_features = np.asarray([target.feat for target in self.prune_tracks])
+            feats_dist = cdist(track_features, feat[np.newaxis, :], metric='cosine')
+            if np.amin(feats_dist) < 0.25:  # pruned track cannot update feature for few frames
+                idx = np.argmin(feats_dist)
+                tt = self.prune_tracks[idx]
+                gating = gate_meas_gms_idx(z[np.newaxis, :], feat[np.newaxis, :], model, tt.m, tt.P, tt.feat)
+                if len(gating) > 0:  # associated measurement must be closed to a pruned track
+                    tt.re_activate(z, feat, prob_birth)
+                    self.tt_lmb.append(tt)
+                    self.prune_tracks.remove(tt)
+                    return True
+        false_meas = False
+        # first, checking whether new measurement overlap with existing tracks
+        ious = bbox_iou_xyah(z, self.tt_lmb_xyah)
+        iou_idx = np.nonzero(ious > 0.2)[0]
+        if len(iou_idx):  # consider as overlap with any existing tracks
+            # second, compare re-id feature cdist with activating tracks
+            track_features = np.asarray([self.tt_lmb[idx].feat for idx in iou_idx])
+            feats_dist = cdist(track_features, feat[np.newaxis, :], metric='cosine')
+            if np.amin(feats_dist) < 0.2:  # consider two re-identification features are similar
+                # new measurement and an existing track have similar feature, ignore this measurement
+                false_meas = True
+        return false_meas
+
+    def reappear_tracks(self, assign_prob, z, feat, b_idx, model):
+        re_activate = False
+        if len(self.prune_tracks) == 0 or len(feat) == 0:
+            return re_activate
+        track_features = np.asarray([target.feat for target in self.prune_tracks])
+        tt_feat_dist = cdist(track_features, feat)
+        tt_feat_dist = 0.05 * tt_feat_dist * 2 + 0.95 * (2 - tt_feat_dist) * 2
+        cost = tt_feat_dist * np.tile(1 - assign_prob, (len(self.prune_tracks), 1))
+        assignment_index = lap.lapjv(-np.log(cost), extend_cost=True, cost_limit=-0.5)
+        b_idx_select = np.ones(len(b_idx), dtype=bool)
+        for tt_idx, meas_idx in enumerate(assignment_index[1]):
+            if meas_idx < 0:
+                continue
+            target = self.prune_tracks[tt_idx]
+            target.re_activate(z[meas_idx], feat[meas_idx],
+                               min(model.prob_birth, cost[tt_idx, meas_idx] / np.sum(cost)))
+            self.tt_birth.append(target)
+            b_idx_select[meas_idx] = False
+        return b_idx_select
+
+    def apdative_birth(self, assign_prob, z, feat, model, k):
+        not_assigned_sum = sum(1 - assign_prob) + np.spacing(1)  # make sure this sum is not zero
+        b_idx = np.nonzero(assign_prob < self.model.b_thresh)[0]
+        self.tt_birth = []
+        for idx, meas_idx in enumerate(b_idx):
+            # eq (75) "The Labeled Multi-Bernoulli Filter", Stephan Reuter∗, Ba-Tuong Vo, Ba-Ngu Vo, ...
+            prob_birth = min(model.prob_birth, (1 - assign_prob[meas_idx]) / not_assigned_sum * model.lambda_b)
+            prob_birth = max(prob_birth, np.spacing(1))  # avoid zero birth probability
+
+            re_activate = self.re_activate_tracks(z[meas_idx], feat[meas_idx], model, prob_birth)
+            if re_activate:
+                continue
+
+            target = Target(z[meas_idx], feat[meas_idx], prob_birth, self.id, self.use_feat)
+            self.id += 1  # or label = str(k + 1) + '.' + str(idx)
+            self.tt_birth.append(target)
+        # END
+
+    def clean_lmb(self, model, tim_step):
+        # prune tracks with low existence probabilities
+
+        # extract vector of existence probabilities from LMB track table
+        rvect = np.array([tt.r for tt in self.tt_lmb])
+
+        idxkeep = np.nonzero(rvect > model.track_threshold)[0]
+        tt_lmb_out = [self.tt_lmb[i] for i in idxkeep]
+        idxprune = np.nonzero(rvect <= model.track_threshold)[0]
+        self.prune_tracks = self.prune_tracks + [self.tt_lmb[i] for i in idxprune]
+        remove = []
+        for t in self.prune_tracks:
+            if tim_step - t.last_active > 50:
+                remove.append(t)
+        for t in remove:
+            self.prune_tracks.remove(t)
+
+        # cleanup tracks
+        for target in tt_lmb_out:
+            target.cleanup()
+
+        self.tt_lmb = tt_lmb_out
+
+    # END clean_lmb
+
+    def extract_estimates(self):
+        # extract estimates via MAP cardinality and corresponding tracks
+        num_tracks = len(self.tt_lmb)
+        rvect = np.array([tt.r for tt in self.tt_lmb])
+        rvect = np.minimum(rvect, 1. - 1e-6)
+        rvect = np.maximum(rvect, 1e-6)
+        # Calculate the cardinality distribution of the multi-Bernoulli RFS
+        cdn = esf(rvect / (1 - rvect))  # np.prod(1 - rvect) * esf(rvect / (1 - rvect))
+        mode = np.argmax(cdn)
+        N = min(len(rvect), mode)
+        idxcmp = np.argsort(-rvect)
+        X, L = np.zeros((4, num_tracks)), np.zeros(num_tracks, dtype=int)
+        select_idx = 0
+        for n in range(N):
+            select_target = self.tt_lmb[idxcmp[n]]
+            idxtrk = np.argmax(select_target.w)
+            X[:, select_idx] = select_target.m[:4, idxtrk]
+            L[select_idx] = select_target.l
+            select_idx += 1
+
+        # hysteresis, eq (71) "The Labeled Multi-Bernoulli Filter", Stephan Reuter∗, Ba-Tuong Vo, Ba-Ngu Vo, ...
+        for idxx in range(N, num_tracks):
+            select_target = self.tt_lmb[idxcmp[idxx]]
+            if select_target.r_max > 0.7 and select_target.r > 0.1:
+                idxtrk = np.argmax(select_target.w)
+                X[:, select_idx] = select_target.m[:4, idxtrk]
+                L[select_idx] = select_target.l
+                select_idx += 1
+        X[2, :] = np.clip(X[2, :], 0.15, None)  # constraint 'a' not to be negative
+        if select_idx > 0:
+            self.average_area = sum(X[2, :] * X[3, :] ** 2) / select_idx
+        return X[:, :select_idx], L[:select_idx]
+
+    def update(self, fdets, img):
+        #####
+        remain_inds = fdets[:, 4] > self.track_thresh
+        z, feat = fdets[remain_inds, 0:4], fdets[remain_inds, 5:]
+        # Input z : (n, 4), number of measurements and Top, Left, Bottom, Right of a bounding box
+        # Input feat : (n, reid_dim), z[i, :] has re-id feature feat[i, :], norm2 feature
+        # tlbr to cxcyah
+        z[:, 2:4] -= z[:, 0:2]
+        z[:, 0:2] += z[:, 2:4] / 2
+        z[:, 2] = z[:, 2] / z[:, 3]
+
+        # joint predict and update, results in GLMB, convert to LMB
+        self.jointlmbpredictupdate(self.model, z, feat, self.frame)
+
+        # pruning, truncation and track cleanup
+        self.clean_lmb(self.model, self.frame)
+
+        # state estimation
+        X, L = self.extract_estimates()
+        self.frame = self.frame + 1
+        X[2, :] = X[2, :] * X[3, :]  # xyah to xywh
+        X[0, :], X[1, :] = X[0, :] - X[2, :] / 2, X[1, :] - X[3, :] / 2  # xywh to tlwh
+        X[2, :], X[3, :] = X[0, :] + X[2, :], X[1, :] + X[3, :]  # tlwh to tlrb
+
+        return [Track(tid, X[:, idx], 1) for idx, tid in enumerate(L)]
+    # END
diff --git a/trackers/joint_lmb/utils.py b/trackers/joint_lmb/utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..1c6cdf31c8f1e21316179590208f1b46954e5765
--- /dev/null
+++ b/trackers/joint_lmb/utils.py
@@ -0,0 +1,280 @@
+import numpy as np
+from scipy.linalg import cholesky
+from cpputils import Murty
+from scipy.spatial.distance import cdist
+from scipy.stats import multivariate_normal
+
+
+def kalman_predict_multiple_noloop(model, m, P):
+    plength = m.shape[1]
+
+    m_predict = model.F @ m
+    P_predict = np.stack([model.Q] * plength) + np.matmul((model.F @ P).transpose(2, 1, 0), model.F.T)
+    P_predict = P_predict.transpose(1, 2, 0)
+
+    return m_predict, P_predict
+
+def kalman_update_multiple_noloop(z, model, m, P):
+    plength = m.shape[1]
+    P = P.transpose(2, 0, 1)
+    y = np.stack([z] * plength) - (model.H @ m).T
+    y = y[:, :, np.newaxis]
+    S = np.stack([model.R] * plength) + np.matmul(model.H @ P, model.H.T)
+    invS = np.linalg.inv(S)
+    K = np.matmul(P @ model.H.T, invS)
+
+    mn = m + np.squeeze(K @ y, axis=2).T
+    Pn = P - np.matmul(K @ S, K.transpose(0, 2, 1))
+
+    yInvSy = np.squeeze(np.matmul(y.transpose(0, 2, 1), invS @ y), axis=(1, 2))
+    qz = np.exp(-0.5 * len(z) * np.log(2 * np.pi) - 0.5 * np.log(np.linalg.det(S)) - 0.5 * yInvSy)
+
+    return qz, mn, Pn.transpose(1,2,0)
+
+def kalman_predict_multiple(model, m, P):
+    plength = m.shape[1];
+
+    m_predict = np.zeros(m.shape);
+    P_predict = np.zeros(P.shape);
+
+    for idxp in range(0, plength):
+        m_temp, P_temp = kalman_predict_single(model.F, model.Q, m[:, idxp], P[:, :, idxp]);
+        m_predict[:, idxp] = m_temp;
+        P_predict[:, :, idxp] = P_temp;
+
+    return m_predict, P_predict
+
+
+def kalman_predict_single(F, Q, m, P):
+    m_predict = np.dot(F, m)
+    P_predict = Q + np.dot(F, np.dot(P, F.T))
+    return m_predict, P_predict
+
+
+def gate_meas_gms_idx(z, feat, model, m, P, tt_feat):
+    zlength, plength = z.shape[0], m.shape[1]
+    if zlength == 0:
+        return np.empty(0)
+    valid_idx = np.zeros(zlength, dtype=bool)
+    cdist_tmp = cdist(feat, tt_feat[np.newaxis, :], metric='cosine').flatten()
+    for j in range(plength):
+        Sj = model.R + np.dot(np.dot(model.H, P[:, :, j]), model.H.T)
+        Vs = cholesky(Sj)
+        inv_sqrt_Sj = np.linalg.inv(Vs)
+        nu = z.T - np.tile(np.dot(model.H, m[:, j].reshape(-1, 1)), zlength)
+        dist = sum(np.square(np.dot(inv_sqrt_Sj, nu)))
+
+        valid_idx_tmp = np.nonzero(np.logical_or(dist < model.gamma, cdist_tmp < 0.3))[0]
+        valid_idx[valid_idx_tmp] = True
+
+    return np.nonzero(valid_idx)[0]
+
+def kalman_update_multiple(z, model, m, P):
+    plength = m.shape[1]
+
+    qz_update = np.zeros(plength)
+    m_update = np.zeros((model.x_dim, plength))
+    P_update = np.zeros((model.x_dim, model.x_dim, plength))
+
+    for idxp in range(0, plength):
+        qz_temp, m_temp, P_temp = kalman_update_single(z, model.H, model.R, m[:, idxp], P[:, :, idxp])
+        qz_update[idxp] = qz_temp
+        m_update[:, idxp] = m_temp.flatten()
+        P_update[:, :, idxp] = P_temp
+
+    return qz_update, m_update, P_update
+
+
+def kalman_update_single(z, H, R, m, P):
+    mu = np.dot(H, m)
+    S = R + np.dot(np.dot(H, P), H.T)
+    Vs = np.linalg.cholesky(S);
+    # det_S = np.prod(np.diag(Vs)) ** 2;
+    inv_sqrt_S = np.linalg.inv(Vs);
+    iS = np.dot(inv_sqrt_S, inv_sqrt_S.T)
+    K = np.dot(np.dot(P, H.T), iS)
+
+    z_mu = z - mu
+    qz_temp = multivariate_normal.pdf(z, mean=mu, cov=S)
+    m_temp = m + np.dot(K, z_mu)
+    P_temp = np.dot((np.eye(len(P)) - np.dot(K, H)), P)
+
+    return qz_temp, m_temp, P_temp
+
+def gibbswrap_jointpredupdt_custom(P0, m):
+    n1 = P0.shape[0];
+
+    if m == 0:
+        m = 1 # return at least one solution
+
+    assignments = np.zeros((m, n1));
+    costs = np.zeros(m);
+
+    currsoln = np.arange(n1, 2 * n1);  # use all missed detections as initial solution
+    assignments[0, :] = currsoln;
+    costs[0] = sum(P0[np.arange(0, n1), currsoln])
+    for sol in range(1, m):
+        for var in range(0, n1):
+            tempsamp = np.exp(-P0[var, :]);  # grab row of costs for current association variable
+            # lock out current and previous iteration step assignments except for the one in question
+            tempsamp[np.delete(currsoln, var)] = 0;
+            idxold = np.nonzero(tempsamp > 0)[0];
+            tempsamp = tempsamp[idxold];
+            currsoln[var] = np.digitize(np.random.rand(1), np.concatenate(([0], np.cumsum(tempsamp) / sum(tempsamp))));
+            currsoln[var] = idxold[currsoln[var]-1];
+        assignments[sol, :] = currsoln;
+        costs[sol] = sum(P0[np.arange(0, n1), currsoln])
+    C, I, _ = np.unique(assignments, return_index=True, return_inverse=True, axis=0);
+    assignments = C;
+    costs = costs[I];
+
+    return assignments, costs
+
+
+def murty(P0, m):
+    n1 = P0.shape[0]
+    if n1 == 0:
+        return np.empty(0), np.empty(0)
+    mgen = Murty(P0)
+    assignments = np.zeros((m, n1))
+    costs = np.zeros(m)
+    sol_idx = 0
+    # for cost, assignment in murty(C_ext):
+    for sol in range(0, m):
+        ok, cost_m, assignment_m = mgen.draw()
+        if (not ok):
+            break
+        assignments[sol, :] = assignment_m
+        costs[sol] = cost_m
+        sol_idx += 1
+    C, I, _ = np.unique(assignments[:sol_idx, :], return_index=True, return_inverse=True, axis=0)
+    assignments = C
+    costs = costs[I]
+    return assignments, costs
+
+def gaus_prune(w, x, P, elim_threshold):
+    idx = np.nonzero(w > elim_threshold)[0]
+    w_new = w[idx]
+    x_new = x[:, idx]
+    P_new = P[:, :, idx]
+    return w_new, x_new, P_new
+
+
+def gaus_merge(w, x, P, threshold):
+    L = len(w)
+    x_dim, max_cmpt = x.shape[0], x.shape[1]
+    I = np.arange(L)
+    w_new, x_new, P_new = np.empty(max_cmpt), np.empty((x_dim, max_cmpt)), np.empty((x_dim, x_dim, max_cmpt))
+    idx = 0
+    if np.count_nonzero(w) == 0:
+        return w_new, x_new, P_new
+
+    while len(I):
+        j = np.argmax(w)
+        Ij = np.empty(0, dtype=int)
+        iPt = np.linalg.inv(P[:, :, j])
+
+        for i in I:
+            xi_xj = x[:, i] - x[:, j]
+            val = np.dot(np.dot(xi_xj.T, iPt), xi_xj)
+            if val <= threshold:
+                Ij = np.append(Ij, i)
+        w_new_t = sum(w[Ij])
+        x_new_t = np.sum(x[:, Ij] * w[Ij], axis=1)
+        P_new_t = np.sum(P[:, :, Ij] * w[Ij], axis=2)
+
+        x_new_t = x_new_t / w_new_t
+        P_new_t = P_new_t / w_new_t
+
+        w_new[idx] = w_new_t
+        x_new[:, idx] = x_new_t
+        P_new[:, :, idx] = P_new_t
+        idx += 1
+
+        I = np.setdiff1d(I, Ij)
+        w[Ij] = -1
+
+    return w_new[:idx], x_new[:, :idx], P_new[:, :, :idx]
+
+def gaus_cap(w, x, P, max_number):
+    if len(w) > max_number:
+        idx = np.argsort(-w)
+        w_new = w[idx[:max_number]]
+        w = w_new * (sum(w)/sum(w_new))
+        x = x[:, idx[:max_number]]
+        P = P[:, :, idx[:max_number]]
+    return w, x, P
+
+def esf(Z):
+    """
+    Calculate elementary symmetric function using Mahler's recursive formula
+
+    cardinality 1: r1 + r2 + .. + rn
+    cardinality 2: r1*r2 + r1*3 + ... + r2*3 + ..
+
+    Parameters
+    ----------
+    Z: array_like
+        Input vector
+
+    Returns
+    -------
+    out: ndarray
+    """
+    n_z = len(Z)
+    if n_z == 0:
+        return np.ones(1)
+
+    F = np.zeros((2, n_z))
+    i_n = 0
+    i_n_minus = 1
+
+    for n in range(n_z):
+        F[i_n, 0] = F[i_n_minus, 0] + Z[n]
+        for k in range(1, n + 1):
+            if k == n:
+                F[i_n, k] = Z[n] * F[i_n_minus, k - 1]
+            else:
+                F[i_n, k] = F[i_n_minus, k] + Z[n] * F[i_n_minus, k - 1]
+
+        i_n, i_n_minus = i_n_minus, i_n
+
+    return np.concatenate((np.ones(1), F[i_n_minus, :]))
+
+if __name__ == '__main__':
+
+    import os
+    from scipy.io import savemat
+
+    if os.path.exists('./w.npy'):
+        w=np.load('w.npy')
+        x = np.load('x.npy')
+        P = np.load('P.npy')
+    else:
+        w = np.random.dirichlet(np.ones(10))
+        x = np.random.rand(4, 10)*10
+        P = np.random.rand(4,4,10)*10
+
+        savemat('w.mat', {'w':w})
+        savemat('x.mat', {'x': x})
+        savemat('P.mat', {'P': P})
+
+        np.save('w.npy', w)
+        np.save('x.npy', x)
+        np.save('P.npy', P)
+
+    w,x,p = gaus_merge(w,x,P, 4)
+    # x = load('x.mat');
+    # x = x.x;
+    # P = load('P.mat');
+    # P = P.P;
+    # w = load('w.mat');
+    # w = w.w;
+    # w = reshape(w, [10 1]);
+    # [wn, xn, pn] = gaus_merge(w, x, P, 4);
+
+    P0 = np.array([[0.0304592074847086, np.inf, np.inf, np.inf, 7.41858090274813, np.inf, np.inf, np.inf, -0.345108847352739, np.inf, np.inf],
+                   [np.inf, 0.0304592074847086, np.inf, np.inf, np.inf, 7.41858090274813, np.inf, np.inf, np.inf, -0.849090957754662, np.inf],
+                   [np.inf, np.inf, 0.0304592074847086, np.inf, np.inf, np.inf, 7.41858090274813, np.inf, np.inf, np.inf, 1.64038243547480],
+                   [np.inf, np.inf, np.inf, 0.0304592074847086, np.inf, np.inf, np.inf, 7.41858090274813, np.inf, np.inf, np.inf]])
+    gibbswrap_jointpredupdt_custom(P0, 1000)
\ No newline at end of file
diff --git a/trackers/motdt/basetrack.py b/trackers/motdt/basetrack.py
new file mode 100644
index 0000000000000000000000000000000000000000..f06729249983366b05dcd8acbc2dd9e3232d1b2d
--- /dev/null
+++ b/trackers/motdt/basetrack.py
@@ -0,0 +1,56 @@
+import numpy as np
+from collections import OrderedDict
+
+
+class TrackState(object):
+    New = 0
+    Tracked = 1
+    Lost = 2
+    Removed = 3
+    Replaced = 4
+
+
+class BaseTrack(object):
+    _count = 0
+
+    track_id = 0
+    is_activated = False
+    state = TrackState.New
+
+    history = OrderedDict()
+    features = []
+    curr_feature = None
+    score = 0
+    start_frame = 0
+    frame_id = 0
+    time_since_update = 0
+
+    # multi-camera
+    location = (np.inf, np.inf)
+
+    @property
+    def end_frame(self):
+        return self.frame_id
+
+    @staticmethod
+    def next_id():
+        BaseTrack._count += 1
+        return BaseTrack._count
+
+    def activate(self, *args):
+        raise NotImplementedError
+
+    def predict(self):
+        raise NotImplementedError
+
+    def update(self, *args, **kwargs):
+        raise NotImplementedError
+
+    def mark_lost(self):
+        self.state = TrackState.Lost
+
+    def mark_removed(self):
+        self.state = TrackState.Removed
+
+    def mark_replaced(self):
+        self.state = TrackState.Replaced
diff --git a/trackers/motdt/kalman_filter.py b/trackers/motdt/kalman_filter.py
new file mode 100644
index 0000000000000000000000000000000000000000..496b937a9f76f726af37f00da53befd8d0bf59fb
--- /dev/null
+++ b/trackers/motdt/kalman_filter.py
@@ -0,0 +1,272 @@
+# vim: expandtab:ts=4:sw=4
+import numpy as np
+import scipy.linalg
+
+
+"""
+Table for the 0.95 quantile of the chi-square distribution with N degrees of
+freedom (contains values for N=1, ..., 9). Taken from MATLAB/Octave's chi2inv
+function and used as Mahalanobis gating threshold.
+"""
+chi2inv95 = {
+    1: 3.8415,
+    2: 5.9915,
+    3: 7.8147,
+    4: 9.4877,
+    5: 11.070,
+    6: 12.592,
+    7: 14.067,
+    8: 15.507,
+    9: 16.919,
+}
+
+
+class KalmanFilter(object):
+    """
+    A simple Kalman filter for tracking bounding boxes in image space.
+
+    The 8-dimensional state space
+
+        x, y, a, h, vx, vy, va, vh
+
+    contains the bounding box center position (x, y), aspect ratio a, height h,
+    and their respective velocities.
+
+    Object motion follows a constant velocity model. The bounding box location
+    (x, y, a, h) is taken as direct observation of the state space (linear
+    observation model).
+
+    """
+
+    def __init__(self):
+        ndim, dt = 4, 1.0
+
+        # Create Kalman filter model matrices.
+        self._motion_mat = np.eye(2 * ndim, 2 * ndim)
+        for i in range(ndim):
+            self._motion_mat[i, ndim + i] = dt
+        self._update_mat = np.eye(ndim, 2 * ndim)
+
+        # Motion and observation uncertainty are chosen relative to the current
+        # state estimate. These weights control the amount of uncertainty in
+        # the model. This is a bit hacky.
+        self._std_weight_position = 1.0 / 20
+        self._std_weight_velocity = 1.0 / 160
+
+    def initiate(self, measurement):
+        """Create track from unassociated measurement.
+
+        Parameters
+        ----------
+        measurement : ndarray
+            Bounding box coordinates (x, y, a, h) with center position (x, y),
+            aspect ratio a, and height h.
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector (8 dimensional) and covariance matrix (8x8
+            dimensional) of the new track. Unobserved velocities are initialized
+            to 0 mean.
+
+        """
+        mean_pos = measurement
+        mean_vel = np.zeros_like(mean_pos)
+        mean = np.r_[mean_pos, mean_vel]
+
+        std = [
+            2 * self._std_weight_position * measurement[3],
+            2 * self._std_weight_position * measurement[3],
+            1e-2,
+            2 * self._std_weight_position * measurement[3],
+            10 * self._std_weight_velocity * measurement[3],
+            10 * self._std_weight_velocity * measurement[3],
+            1e-5,
+            10 * self._std_weight_velocity * measurement[3],
+        ]
+        covariance = np.diag(np.square(std))
+        return mean, covariance
+
+    def predict(self, mean, covariance):
+        """Run Kalman filter prediction step.
+
+        Parameters
+        ----------
+        mean : ndarray
+            The 8 dimensional mean vector of the object state at the previous
+            time step.
+        covariance : ndarray
+            The 8x8 dimensional covariance matrix of the object state at the
+            previous time step.
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector and covariance matrix of the predicted
+            state. Unobserved velocities are initialized to 0 mean.
+
+        """
+        std_pos = [
+            self._std_weight_position * mean[3],
+            self._std_weight_position * mean[3],
+            1e-2,
+            self._std_weight_position * mean[3],
+        ]
+        std_vel = [
+            self._std_weight_velocity * mean[3],
+            self._std_weight_velocity * mean[3],
+            1e-5,
+            self._std_weight_velocity * mean[3],
+        ]
+        motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))
+
+        # mean = np.dot(self._motion_mat, mean)
+        mean = np.dot(mean, self._motion_mat.T)
+        covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov
+
+        return mean, covariance
+
+    def project(self, mean, covariance):
+        """Project state distribution to measurement space.
+
+        Parameters
+        ----------
+        mean : ndarray
+            The state's mean vector (8 dimensional array).
+        covariance : ndarray
+            The state's covariance matrix (8x8 dimensional).
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the projected mean and covariance matrix of the given state
+            estimate.
+
+        """
+        std = [
+            self._std_weight_position * mean[3],
+            self._std_weight_position * mean[3],
+            1e-1,
+            self._std_weight_position * mean[3],
+        ]
+        innovation_cov = np.diag(np.square(std))
+
+        mean = np.dot(self._update_mat, mean)
+        covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
+        return mean, covariance + innovation_cov
+
+    def multi_predict(self, mean, covariance):
+        """Run Kalman filter prediction step (Vectorized version).
+        Parameters
+        ----------
+        mean : ndarray
+            The Nx8 dimensional mean matrix of the object states at the previous
+            time step.
+        covariance : ndarray
+            The Nx8x8 dimensional covariance matrics of the object states at the
+            previous time step.
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the mean vector and covariance matrix of the predicted
+            state. Unobserved velocities are initialized to 0 mean.
+        """
+        std_pos = [
+            self._std_weight_position * mean[:, 3],
+            self._std_weight_position * mean[:, 3],
+            1e-2 * np.ones_like(mean[:, 3]),
+            self._std_weight_position * mean[:, 3],
+        ]
+        std_vel = [
+            self._std_weight_velocity * mean[:, 3],
+            self._std_weight_velocity * mean[:, 3],
+            1e-5 * np.ones_like(mean[:, 3]),
+            self._std_weight_velocity * mean[:, 3],
+        ]
+        sqr = np.square(np.r_[std_pos, std_vel]).T
+
+        motion_cov = []
+        for i in range(len(mean)):
+            motion_cov.append(np.diag(sqr[i]))
+        motion_cov = np.asarray(motion_cov)
+
+        mean = np.dot(mean, self._motion_mat.T)
+        left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
+        covariance = np.dot(left, self._motion_mat.T) + motion_cov
+
+        return mean, covariance
+
+    def update(self, mean, covariance, measurement):
+        """Run Kalman filter correction step.
+
+        Parameters
+        ----------
+        mean : ndarray
+            The predicted state's mean vector (8 dimensional).
+        covariance : ndarray
+            The state's covariance matrix (8x8 dimensional).
+        measurement : ndarray
+            The 4 dimensional measurement vector (x, y, a, h), where (x, y)
+            is the center position, a the aspect ratio, and h the height of the
+            bounding box.
+
+        Returns
+        -------
+        (ndarray, ndarray)
+            Returns the measurement-corrected state distribution.
+
+        """
+        projected_mean, projected_cov = self.project(mean, covariance)
+
+        chol_factor, lower = scipy.linalg.cho_factor(projected_cov, lower=True, check_finite=False)
+        kalman_gain = scipy.linalg.cho_solve(
+            (chol_factor, lower),
+            np.dot(covariance, self._update_mat.T).T,
+            check_finite=False,
+        ).T
+        innovation = measurement - projected_mean
+
+        new_mean = mean + np.dot(innovation, kalman_gain.T)
+        new_covariance = covariance - np.linalg.multi_dot((kalman_gain, projected_cov, kalman_gain.T))
+        return new_mean, new_covariance
+
+    def gating_distance(self, mean, covariance, measurements, only_position=False, metric="maha"):
+        """Compute gating distance between state distribution and measurements.
+        A suitable distance threshold can be obtained from `chi2inv95`. If
+        `only_position` is False, the chi-square distribution has 4 degrees of
+        freedom, otherwise 2.
+        Parameters
+        ----------
+        mean : ndarray
+            Mean vector over the state distribution (8 dimensional).
+        covariance : ndarray
+            Covariance of the state distribution (8x8 dimensional).
+        measurements : ndarray
+            An Nx4 dimensional matrix of N measurements, each in
+            format (x, y, a, h) where (x, y) is the bounding box center
+            position, a the aspect ratio, and h the height.
+        only_position : Optional[bool]
+            If True, distance computation is done with respect to the bounding
+            box center position only.
+        Returns
+        -------
+        ndarray
+            Returns an array of length N, where the i-th element contains the
+            squared Mahalanobis distance between (mean, covariance) and
+            `measurements[i]`.
+        """
+        mean, covariance = self.project(mean, covariance)
+        if only_position:
+            mean, covariance = mean[:2], covariance[:2, :2]
+            measurements = measurements[:, :2]
+
+        d = measurements - mean
+        if metric == "gaussian":
+            return np.sum(d * d, axis=1)
+        elif metric == "maha":
+            cholesky_factor = np.linalg.cholesky(covariance)
+            z = scipy.linalg.solve_triangular(cholesky_factor, d.T, lower=True, check_finite=False, overwrite_b=True)
+            squared_maha = np.sum(z * z, axis=0)
+            return squared_maha
+        else:
+            raise ValueError("invalid distance metric")
diff --git a/trackers/motdt/matching.py b/trackers/motdt/matching.py
new file mode 100644
index 0000000000000000000000000000000000000000..bf43e0d17565cb6b406b7f25a58488727656ea3e
--- /dev/null
+++ b/trackers/motdt/matching.py
@@ -0,0 +1,119 @@
+import cv2
+import numpy as np
+import lap
+from scipy.spatial.distance import cdist
+
+from cython_bbox import bbox_overlaps as bbox_ious
+from . import kalman_filter
+
+
+def _indices_to_matches(cost_matrix, indices, thresh):
+    matched_cost = cost_matrix[tuple(zip(*indices))]
+    matched_mask = matched_cost <= thresh
+
+    matches = indices[matched_mask]
+    unmatched_a = tuple(set(range(cost_matrix.shape[0])) - set(matches[:, 0]))
+    unmatched_b = tuple(set(range(cost_matrix.shape[1])) - set(matches[:, 1]))
+
+    return matches, unmatched_a, unmatched_b
+
+
+def linear_assignment(cost_matrix, thresh):
+    if cost_matrix.size == 0:
+        return (
+            np.empty((0, 2), dtype=int),
+            tuple(range(cost_matrix.shape[0])),
+            tuple(range(cost_matrix.shape[1])),
+        )
+    matches, unmatched_a, unmatched_b = [], [], []
+    cost, x, y = lap.lapjv(cost_matrix, extend_cost=True, cost_limit=thresh)
+    for ix, mx in enumerate(x):
+        if mx >= 0:
+            matches.append([ix, mx])
+    unmatched_a = np.where(x < 0)[0]
+    unmatched_b = np.where(y < 0)[0]
+    matches = np.asarray(matches)
+    return matches, unmatched_a, unmatched_b
+
+
+def ious(atlbrs, btlbrs):
+    """
+    Compute cost based on IoU
+    :type atlbrs: list[tlbr] | np.ndarray
+    :type atlbrs: list[tlbr] | np.ndarray
+    :rtype ious np.ndarray
+    """
+    ious = np.zeros((len(atlbrs), len(btlbrs)), dtype=np.float)
+    if ious.size == 0:
+        return ious
+
+    ious = bbox_ious(
+        np.ascontiguousarray(atlbrs, dtype=np.float),
+        np.ascontiguousarray(btlbrs, dtype=np.float),
+    )
+
+    return ious
+
+
+def iou_distance(atracks, btracks):
+    """
+    Compute cost based on IoU
+    :type atracks: list[STrack]
+    :type btracks: list[STrack]
+    :rtype cost_matrix np.ndarray
+    """
+    atlbrs = [track.tlbr for track in atracks]
+    btlbrs = [track.tlbr for track in btracks]
+    _ious = ious(atlbrs, btlbrs)
+    cost_matrix = 1 - _ious
+
+    return cost_matrix
+
+
+def nearest_reid_distance(tracks, detections, metric="cosine"):
+    """
+    Compute cost based on ReID features
+    :type tracks: list[STrack]
+    :type detections: list[BaseTrack]
+    :rtype cost_matrix np.ndarray
+    """
+    cost_matrix = np.zeros((len(tracks), len(detections)), dtype=np.float)
+    if cost_matrix.size == 0:
+        return cost_matrix
+
+    det_features = np.asarray([track.curr_feature for track in detections], dtype=np.float32)
+    for i, track in enumerate(tracks):
+        cost_matrix[i, :] = np.maximum(0.0, cdist(track.features, det_features, metric).min(axis=0))
+
+    return cost_matrix
+
+
+def mean_reid_distance(tracks, detections, metric="cosine"):
+    """
+    Compute cost based on ReID features
+    :type tracks: list[STrack]
+    :type detections: list[BaseTrack]
+    :type metric: str
+    :rtype cost_matrix np.ndarray
+    """
+    cost_matrix = np.empty((len(tracks), len(detections)), dtype=np.float)
+    if cost_matrix.size == 0:
+        return cost_matrix
+
+    track_features = np.asarray([track.curr_feature for track in tracks], dtype=np.float32)
+    det_features = np.asarray([track.curr_feature for track in detections], dtype=np.float32)
+    cost_matrix = cdist(track_features, det_features, metric)
+
+    return cost_matrix
+
+
+def gate_cost_matrix(kf, cost_matrix, tracks, detections, only_position=False):
+    if cost_matrix.size == 0:
+        return cost_matrix
+    gating_dim = 2 if only_position else 4
+    gating_threshold = kalman_filter.chi2inv95[gating_dim]
+    measurements = np.asarray([det.to_xyah() for det in detections])
+    for row, track in enumerate(tracks):
+        gating_distance = kf.gating_distance(track.mean, track.covariance, measurements, only_position)
+        cost_matrix[row, gating_distance > gating_threshold] = np.inf
+    return cost_matrix
diff --git a/trackers/motdt/motdt_tracker.py b/trackers/motdt/motdt_tracker.py
new file mode 100644
index 0000000000000000000000000000000000000000..37485bcecf2f643a9f9276dad50f7fecf18d55f3
--- /dev/null
+++ b/trackers/motdt/motdt_tracker.py
@@ -0,0 +1,326 @@
+import numpy as np
+
+# from numba import jit
+from collections import OrderedDict, deque
+import itertools
+
+from . import matching
+from .kalman_filter import KalmanFilter
+
+from .basetrack import BaseTrack, TrackState
+
+
+class STrack(BaseTrack):
+    def __init__(self, tlwh, score, max_n_features=100, from_det=True):
+
+        # wait activate
+        self._tlwh = np.asarray(tlwh, dtype=np.float)
+        self.kalman_filter = None
+        self.mean, self.covariance = None, None
+        self.is_activated = False
+
+        self.score = score
+        self.max_n_features = max_n_features
+        self.curr_feature = None
+        self.last_feature = None
+        self.features = deque([], maxlen=self.max_n_features)
+
+        # classification
+        self.from_det = from_det
+        self.tracklet_len = 0
+        self.time_by_tracking = 0
+
+        # self-tracking
+        self.tracker = None
+
+    def set_feature(self, feature):
+        if feature is None:
+            return False
+        self.features.append(feature)
+        self.curr_feature = feature
+        self.last_feature = feature
+        # self._p_feature = 0
+        return True
+
+    def predict(self):
+        if self.time_since_update > 0:
+            self.tracklet_len = 0
+
+        self.time_since_update += 1
+
+        mean_state = self.mean.copy()
+        if self.state != TrackState.Tracked:
+            mean_state[7] = 0
+        self.mean, self.covariance = self.kalman_filter.predict(mean_state, self.covariance)
+
+        if self.tracker:
+            self.tracker.update_roi(self.tlwh)
+
+    def self_tracking(self, image):
+        tlwh = self.tracker.predict(image) if self.tracker else self.tlwh
+        return tlwh
+
+    def activate(self, kalman_filter, frame_id):
+        """Start a new tracklet"""
+        self.kalman_filter = kalman_filter  # type: KalmanFilter
+        self.track_id = self.next_id()
+        # cx, cy, aspect_ratio, height, dx, dy, da, dh
+        self.mean, self.covariance = self.kalman_filter.initiate(self.tlwh_to_xyah(self._tlwh))
+
+        # self.tracker = sot.SingleObjectTracker()
+        # self.tracker.init(image, self.tlwh)
+
+        del self._tlwh
+
+        self.time_since_update = 0
+        self.time_by_tracking = 0
+        self.tracklet_len = 0
+        self.state = TrackState.Tracked
+        # self.is_activated = True
+        self.frame_id = frame_id
+        self.start_frame = frame_id
+
+    def re_activate(self, new_track, frame_id, new_id=False):
+        # self.mean, self.covariance = self.kalman_filter.initiate(self.tlwh_to_xyah(new_track.tlwh))
+        self.mean, self.covariance = self.kalman_filter.update(
+            self.mean, self.covariance, self.tlwh_to_xyah(new_track.tlwh)
+        )
+        self.time_since_update = 0
+        self.time_by_tracking = 0
+        self.tracklet_len = 0
+        self.state = TrackState.Tracked
+        self.is_activated = True
+        self.frame_id = frame_id
+        if new_id:
+            self.track_id = self.next_id()
+
+        self.set_feature(new_track.curr_feature)
+
+    def update(self, new_track, frame_id, update_feature=True):
+        """
+        Update a matched track
+        :type new_track: STrack
+        :type frame_id: int
+        :type update_feature: bool
+        :return:
+        """
+        self.frame_id = frame_id
+        self.time_since_update = 0
+        if new_track.from_det:
+            self.time_by_tracking = 0
+        else:
+            self.time_by_tracking += 1
+        self.tracklet_len += 1
+
+        new_tlwh = new_track.tlwh
+        self.mean, self.covariance = self.kalman_filter.update(self.mean, self.covariance, self.tlwh_to_xyah(new_tlwh))
+        self.state = TrackState.Tracked
+        self.is_activated = True
+
+        self.score = new_track.score
+
+        if update_feature:
+            self.set_feature(new_track.curr_feature)
+            # if self.tracker:
+            #     self.tracker.update(image, self.tlwh)
+
+    @property
+    # @jit
+    def tlwh(self):
+        """Get current position in bounding box format `(top left x, top left y,
+        width, height)`.
+        """
+        if self.mean is None:
+            return self._tlwh.copy()
+        ret = self.mean[:4].copy()
+        ret[2] *= ret[3]
+        ret[:2] -= ret[2:] / 2
+        return ret
+
+    @property
+    # @jit
+    def tlbr(self):
+        """Convert bounding box to format `(min x, min y, max x, max y)`, i.e.,
+        `(top left, bottom right)`.
+        """
+        ret = self.tlwh.copy()
+        ret[2:] += ret[:2]
+        return ret
+
+    @staticmethod
+    # @jit
+    def tlwh_to_xyah(tlwh):
+        """Convert bounding box to format `(center x, center y, aspect ratio,
+        height)`, where the aspect ratio is `width / height`.
+        """
+        ret = np.asarray(tlwh).copy()
+        ret[:2] += ret[2:] / 2
+        ret[2] /= ret[3]
+        return ret
+
+    def to_xyah(self):
+        return self.tlwh_to_xyah(self.tlwh)
+
+    def tracklet_score(self):
+        # score = (1 - np.exp(-0.6 * self.hit_streak)) * np.exp(-0.03 * self.time_by_tracking)
+
+        score = max(0, 1 - np.log(1 + 0.05 * self.time_by_tracking)) * (self.tracklet_len - self.time_by_tracking > 2)
+        # score = max(0, 1 - np.log(1 + 0.05 * self.n_tracking)) * (1 - np.exp(-0.6 * self.hit_streak))
+        return score
+
+    def __repr__(self):
+        return "OT_{}_({}-{})".format(self.track_id, self.start_frame, self.end_frame)
+
+
+class OnlineTracker(object):
+    def __init__(
+        self,
+        min_cls_score=0.4,
+        min_ap_dist=0.8,
+        max_time_lost=30,
+        use_tracking=False,
+        use_refind=True,
+    ):
+
+        self.min_cls_score = min_cls_score
+        self.min_ap_dist = min_ap_dist
+        self.max_time_lost = max_time_lost
+
+        self.kalman_filter = KalmanFilter()
+
+        self.tracked_stracks = []  # type: list[STrack]
+        self.lost_stracks = []  # type: list[STrack]
+        self.removed_stracks = []  # type: list[STrack]
+
+        self.use_refind = use_refind
+        self.use_tracking = use_tracking
+        self.classifier = None
+        # self.reid_model = load_reid_model(model_folder)
+
+        self.frame_id = 0
+
+    def update(self, fdets, img):
+        #####
+        remain_inds = fdets[:, 4] > self.min_cls_score
+        dets, det_scores, features = fdets[remain_inds, 0:4], fdets[remain_inds, 4], fdets[remain_inds, 5:]
+        tlwhs = self._xyxy_to_tlwh_array(dets)
+        self.frame_id += 1
+
+        activated_starcks = []
+        refind_stracks = []
+        lost_stracks = []
+        removed_stracks = []
+
+        """step 1: prediction"""
+        for strack in itertools.chain(self.tracked_stracks, self.lost_stracks):
+            strack.predict()
+
+        """step 2: scoring and selection"""
+        if det_scores is None:
+            det_scores = np.ones(len(tlwhs), dtype=float)
+        detections = [STrack(tlwh, score, from_det=True) for tlwh, score in zip(tlwhs, det_scores)]
+        if self.use_tracking:
+            tracks = [
+                STrack(t.tlwh, 0.6 * t.tracklet_score(), from_det=False)
+                for t in itertools.chain(self.tracked_stracks, self.lost_stracks)
+                if t.is_activated
+            ]
+            detections.extend(tracks)
+        pred_dets = [d for d in detections if not d.from_det]
+        detections = [d for d in detections if d.from_det]
+
+        # set features
+        for i, det in enumerate(detections):
+            det.set_feature(features[i])
+
+        """step 3: association for tracked"""
+        # matching for tracked targets
+        unconfirmed = []
+        tracked_stracks = []  # type: list[STrack]
+        for track in self.tracked_stracks:
+            if not track.is_activated:
+                unconfirmed.append(track)
+            else:
+                tracked_stracks.append(track)
+
+        dists = matching.nearest_reid_distance(tracked_stracks, detections, metric="euclidean")
+        dists = matching.gate_cost_matrix(self.kalman_filter, dists, tracked_stracks, detections)
+        matches, u_track, u_detection = matching.linear_assignment(dists, thresh=self.min_ap_dist)
+        for itracked, idet in matches:
+            tracked_stracks[itracked].update(detections[idet], self.frame_id)
+
+        # matching for missing targets
+        detections = [detections[i] for i in u_detection]
+        dists = matching.nearest_reid_distance(self.lost_stracks, detections, metric="euclidean")
+        dists = matching.gate_cost_matrix(self.kalman_filter, dists, self.lost_stracks, detections)
+        matches, u_lost, u_detection = matching.linear_assignment(dists, thresh=self.min_ap_dist)
+        for ilost, idet in matches:
+            track = self.lost_stracks[ilost]  # type: STrack
+            det = detections[idet]
+            track.re_activate(det, self.frame_id, new_id=not self.use_refind)
+            refind_stracks.append(track)
+
+        # remaining tracked
+        # tracked
+        len_det = len(u_detection)
+        detections = [detections[i] for i in u_detection] + pred_dets
+        r_tracked_stracks = [tracked_stracks[i] for i in u_track]
+        dists = matching.iou_distance(r_tracked_stracks, detections)
+        matches, u_track, u_detection = matching.linear_assignment(dists, thresh=0.7)
+        for itracked, idet in matches:
+            r_tracked_stracks[itracked].update(detections[idet], self.frame_id, update_feature=True)
+        for it in u_track:
+            track = r_tracked_stracks[it]
+            track.mark_lost()
+            lost_stracks.append(track)
+
+        # unconfirmed
+        detections = [detections[i] for i in u_detection if i < len_det]
+        dists = matching.iou_distance(unconfirmed, detections)
+        matches, u_unconfirmed, u_detection = matching.linear_assignment(dists, thresh=0.7)
+        for itracked, idet in matches:
+            unconfirmed[itracked].update(detections[idet], self.frame_id, update_feature=True)
+        for it in u_unconfirmed:
+            track = unconfirmed[it]
+            track.mark_removed()
+            removed_stracks.append(track)
+
+        """step 4: init new stracks"""
+        for inew in u_detection:
+            track = detections[inew]
+            if not track.from_det or track.score < 0.6:
+                continue
+            track.activate(self.kalman_filter, self.frame_id)
+            activated_starcks.append(track)
+
+        """step 6: update state"""
+        for track in self.lost_stracks:
+            if self.frame_id - track.end_frame > self.max_time_lost:
+                track.mark_removed()
+                removed_stracks.append(track)
+
+        self.tracked_stracks = [t for t in self.tracked_stracks if t.state == TrackState.Tracked]
+        self.lost_stracks = [t for t in self.lost_stracks if t.state == TrackState.Lost]  # type: list[STrack]
+        self.tracked_stracks.extend(activated_starcks)
+        self.tracked_stracks.extend(refind_stracks)
+        self.lost_stracks.extend(lost_stracks)
+        self.removed_stracks.extend(removed_stracks)
+
+        # output_stracks = self.tracked_stracks + self.lost_stracks
+
+        # get scores of lost tracks
+        output_tracked_stracks = [track for track in self.tracked_stracks if track.is_activated]
+
+        output_stracks = output_tracked_stracks
+
+        return output_stracks
+
+    @staticmethod
+    def _xyxy_to_tlwh_array(bbox_xyxy):
+        if isinstance(bbox_xyxy, np.ndarray):
+            bbox_tlwh = bbox_xyxy.copy()
+        elif isinstance(bbox_xyxy, torch.Tensor):
+            bbox_tlwh = bbox_xyxy.clone()
+        bbox_tlwh[:, 2] = bbox_xyxy[:, 2] - bbox_xyxy[:, 0]
+        bbox_tlwh[:, 3] = bbox_xyxy[:, 3] - bbox_xyxy[:, 1]
+        return bbox_tlwh
diff --git a/trackers/motdt/reid_model.py b/trackers/motdt/reid_model.py
new file mode 100644
index 0000000000000000000000000000000000000000..59524296aeebd44feece10b31703e8f9103dfca7
--- /dev/null
+++ b/trackers/motdt/reid_model.py
@@ -0,0 +1,269 @@
+import cv2
+import numpy as np
+import torch
+from torch.autograd import Variable
+import torch.nn.functional as F
+import torch.nn as nn
+import pickle
+import os
+from torch.nn.modules import CrossMapLRN2d as SpatialCrossMapLRN
+
+# from torch.legacy.nn import SpatialCrossMapLRN as SpatialCrossMapLRNOld
+from torch.autograd import Function, Variable
+from torch.nn import Module
+
+
+def clip_boxes(boxes, im_shape):
+    """
+    Clip boxes to image boundaries.
+    """
+    boxes = np.asarray(boxes)
+    if boxes.shape[0] == 0:
+        return boxes
+    boxes = np.copy(boxes)
+    # x1 >= 0
+    boxes[:, 0::4] = np.maximum(np.minimum(boxes[:, 0::4], im_shape[1] - 1), 0)
+    # y1 >= 0
+    boxes[:, 1::4] = np.maximum(np.minimum(boxes[:, 1::4], im_shape[0] - 1), 0)
+    # x2 < im_shape[1]
+    boxes[:, 2::4] = np.maximum(np.minimum(boxes[:, 2::4], im_shape[1] - 1), 0)
+    # y2 < im_shape[0]
+    boxes[:, 3::4] = np.maximum(np.minimum(boxes[:, 3::4], im_shape[0] - 1), 0)
+    return boxes
+
+
+def load_net(fname, net, prefix="", load_state_dict=False):
+    import h5py
+
+    with h5py.File(fname, mode="r") as h5f:
+        h5f_is_module = True
+        for k in h5f.keys():
+            if not str(k).startswith("module."):
+                h5f_is_module = False
+                break
+        if prefix == "" and not isinstance(net, nn.DataParallel) and h5f_is_module:
+            prefix = "module."
+
+        for k, v in net.state_dict().items():
+            k = prefix + k
+            if k in h5f:
+                param = torch.from_numpy(np.asarray(h5f[k]))
+                if v.size() != param.size():
+                    print("Inconsistent shape: {}, {}".format(v.size(), param.size()))
+                else:
+                    v.copy_(param)
+            else:
+                print.warning("No layer: {}".format(k))
+
+        epoch = h5f.attrs["epoch"] if "epoch" in h5f.attrs else -1
+
+        if not load_state_dict:
+            if "learning_rates" in h5f.attrs:
+                lr = h5f.attrs["learning_rates"]
+            else:
+                lr = h5f.attrs.get("lr", -1)
+                lr = np.asarray([lr] if lr > 0 else [], dtype=np.float)
+
+            return epoch, lr
+
+        state_file = fname + ".optimizer_state.pk"
+        if os.path.isfile(state_file):
+            with open(state_file, "rb") as f:
+                state_dicts = pickle.load(f)
+                if not isinstance(state_dicts, list):
+                    state_dicts = [state_dicts]
+        else:
+            state_dicts = None
+        return epoch, state_dicts
+
+
+# class SpatialCrossMapLRNFunc(Function):
+
+#     def __init__(self, size, alpha=1e-4, beta=0.75, k=1):
+#         self.size = size
+#         self.alpha = alpha
+#         self.beta = beta
+#         self.k = k
+
+#     def forward(self, input):
+#         self.save_for_backward(input)
+#         self.lrn = SpatialCrossMapLRNOld(self.size, self.alpha, self.beta, self.k)
+#         self.lrn.type(input.type())
+#         return self.lrn.forward(input)
+
+#     def backward(self, grad_output):
+#         input, = self.saved_tensors
+#         return self.lrn.backward(input, grad_output)
+
+
+# # use this one instead
+# class SpatialCrossMapLRN(Module):
+#     def __init__(self, size, alpha=1e-4, beta=0.75, k=1):
+#         super(SpatialCrossMapLRN, self).__init__()
+#         self.size = size
+#         self.alpha = alpha
+#         self.beta = beta
+#         self.k = k
+
+#     def forward(self, input):
+#         return SpatialCrossMapLRNFunc(self.size, self.alpha, self.beta, self.k)(input)
+
+
+class Inception(nn.Module):
+    def __init__(self, in_planes, n1x1, n3x3red, n3x3, n5x5red, n5x5, pool_planes):
+        super(Inception, self).__init__()
+        # 1x1 conv branch
+        self.b1 = nn.Sequential(
+            nn.Conv2d(in_planes, n1x1, kernel_size=1),
+            nn.ReLU(True),
+        )
+
+        # 1x1 conv -> 3x3 conv branch
+        self.b2 = nn.Sequential(
+            nn.Conv2d(in_planes, n3x3red, kernel_size=1),
+            nn.ReLU(True),
+            nn.Conv2d(n3x3red, n3x3, kernel_size=3, padding=1),
+            nn.ReLU(True),
+        )
+
+        # 1x1 conv -> 5x5 conv branch
+        self.b3 = nn.Sequential(
+            nn.Conv2d(in_planes, n5x5red, kernel_size=1),
+            nn.ReLU(True),
+            nn.Conv2d(n5x5red, n5x5, kernel_size=5, padding=2),
+            nn.ReLU(True),
+        )
+
+        # 3x3 pool -> 1x1 conv branch
+        self.b4 = nn.Sequential(
+            nn.MaxPool2d(3, stride=1, padding=1),
+            nn.Conv2d(in_planes, pool_planes, kernel_size=1),
+            nn.ReLU(True),
+        )
+
+    def forward(self, x):
+        y1 = self.b1(x)
+        y2 = self.b2(x)
+        y3 = self.b3(x)
+        y4 = self.b4(x)
+        return torch.cat([y1, y2, y3, y4], 1)
+
+
+class GoogLeNet(nn.Module):
+
+    output_channels = 832
+
+    def __init__(self):
+        super(GoogLeNet, self).__init__()
+        self.pre_layers = nn.Sequential(
+            nn.Conv2d(3, 64, kernel_size=7, stride=2, padding=3),
+            nn.ReLU(True),
+            nn.MaxPool2d(3, stride=2, ceil_mode=True),
+            SpatialCrossMapLRN(5),
+            nn.Conv2d(64, 64, 1),
+            nn.ReLU(True),
+            nn.Conv2d(64, 192, 3, padding=1),
+            nn.ReLU(True),
+            SpatialCrossMapLRN(5),
+            nn.MaxPool2d(3, stride=2, ceil_mode=True),
+        )
+
+        self.a3 = Inception(192, 64, 96, 128, 16, 32, 32)
+        self.b3 = Inception(256, 128, 128, 192, 32, 96, 64)
+
+        self.maxpool = nn.MaxPool2d(3, stride=2, ceil_mode=True)
+
+        self.a4 = Inception(480, 192, 96, 208, 16, 48, 64)
+        self.b4 = Inception(512, 160, 112, 224, 24, 64, 64)
+        self.c4 = Inception(512, 128, 128, 256, 24, 64, 64)
+        self.d4 = Inception(512, 112, 144, 288, 32, 64, 64)
+        self.e4 = Inception(528, 256, 160, 320, 32, 128, 128)
+
+    def forward(self, x):
+        out = self.pre_layers(x)
+        out = self.a3(out)
+        out = self.b3(out)
+        out = self.maxpool(out)
+        out = self.a4(out)
+        out = self.b4(out)
+        out = self.c4(out)
+        out = self.d4(out)
+        out = self.e4(out)
+
+        return out
+
+
+class Model(nn.Module):
+    def __init__(self, n_parts=8):
+        super(Model, self).__init__()
+        self.n_parts = n_parts
+
+        self.feat_conv = GoogLeNet()
+        self.conv_input_feat = nn.Conv2d(self.feat_conv.output_channels, 512, 1)
+
+        # part net
+        self.conv_att = nn.Conv2d(512, self.n_parts, 1)
+
+        for i in range(self.n_parts):
+            setattr(self, "linear_feature{}".format(i + 1), nn.Linear(512, 64))
+
+    def forward(self, x):
+        feature = self.feat_conv(x)
+        feature = self.conv_input_feat(feature)
+
+        att_weights = torch.sigmoid(self.conv_att(feature))
+
+        linear_feautres = []
+        for i in range(self.n_parts):
+            masked_feature = feature * torch.unsqueeze(att_weights[:, i], 1)
+            pooled_feature = F.avg_pool2d(masked_feature, masked_feature.size()[2:4])
+            linear_feautres.append(
+                getattr(self, "linear_feature{}".format(i + 1))(pooled_feature.view(pooled_feature.size(0), -1))
+            )
+
+        concat_features = torch.cat(linear_feautres, 1)
+        normed_feature = concat_features / torch.clamp(torch.norm(concat_features, 2, 1, keepdim=True), min=1e-6)
+
+        return normed_feature
+
+
+def load_reid_model(ckpt):
+    model = Model(n_parts=8)
+    model.inp_size = (80, 160)
+    load_net(ckpt, model)
+    print("Load ReID model from {}".format(ckpt))
+
+    model = model.cuda()
+    model.eval()
+    return model
+
+
+def im_preprocess(image):
+    image = np.asarray(image, np.float32)
+    image -= np.array([104, 117, 123], dtype=np.float32).reshape(1, 1, -1)
+    image = image.transpose((2, 0, 1))
+    return image
+
+
+def extract_image_patches(image, bboxes):
+    bboxes = np.round(bboxes).astype(np.int)
+    bboxes = clip_boxes(bboxes, image.shape)
+    patches = [image[box[1] : box[3], box[0] : box[2]] for box in bboxes]
+    return patches
+
+
+def extract_reid_features(reid_model, image, tlbrs):
+    if len(tlbrs) == 0:
+        return torch.FloatTensor()
+
+    patches = extract_image_patches(image, tlbrs)
+    patches = np.asarray(
+        [im_preprocess(cv2.resize(p, reid_model.inp_size)) for p in patches],
+        dtype=np.float32,
+    )
+
+    with torch.no_grad():
+        im_var = Variable(torch.from_numpy(patches))
+        im_var = im_var.cuda()
+        features = reid_model(im_var).data
+    return features
diff --git a/trackers/ocsort/association.py b/trackers/ocsort/association.py
new file mode 100644
index 0000000000000000000000000000000000000000..c40d009cd2dc235a5c41998bc8b6de83ae2e5cc5
--- /dev/null
+++ b/trackers/ocsort/association.py
@@ -0,0 +1,379 @@
+import os
+import numpy as np
+
+
+def iou_batch(bboxes1, bboxes2):
+    """
+    From SORT: Computes IOU between two bboxes in the form [x1,y1,x2,y2]
+    """
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+    
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    o = wh / ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])                                      
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)                                              
+    return(o)  
+
+
+def giou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    union = ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])                                      
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh)  
+    iou = wh / union
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+    wc = xxc2 - xxc1 
+    hc = yyc2 - yyc1 
+    assert((wc > 0).all() and (hc > 0).all())
+    area_enclose = wc * hc 
+    giou = iou - (area_enclose - union) / area_enclose
+    giou = (giou + 1.)/2.0 # resize from (-1,1) to (0,1)
+    return giou
+
+
+def diou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    # calculate the intersection box
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    union = ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])                                      
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh) 
+    iou = wh / union
+    centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
+    centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
+    centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
+    centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
+
+    inner_diag = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+
+    outer_diag = (xxc2 - xxc1) ** 2 + (yyc2 - yyc1) ** 2
+    diou = iou - inner_diag / outer_diag
+
+    return (diou + 1) / 2.0 # resize from (-1,1) to (0,1)
+
+def ciou_batch(bboxes1, bboxes2):
+    """
+    :param bbox_p: predict of bbox(N,4)(x1,y1,x2,y2)
+    :param bbox_g: groundtruth of bbox(N,4)(x1,y1,x2,y2)
+    :return:
+    """
+    # for details should go to https://arxiv.org/pdf/1902.09630.pdf
+    # ensure predict's bbox form
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    # calculate the intersection box
+    xx1 = np.maximum(bboxes1[..., 0], bboxes2[..., 0])
+    yy1 = np.maximum(bboxes1[..., 1], bboxes2[..., 1])
+    xx2 = np.minimum(bboxes1[..., 2], bboxes2[..., 2])
+    yy2 = np.minimum(bboxes1[..., 3], bboxes2[..., 3])
+    w = np.maximum(0., xx2 - xx1)
+    h = np.maximum(0., yy2 - yy1)
+    wh = w * h
+    union = ((bboxes1[..., 2] - bboxes1[..., 0]) * (bboxes1[..., 3] - bboxes1[..., 1])                                      
+        + (bboxes2[..., 2] - bboxes2[..., 0]) * (bboxes2[..., 3] - bboxes2[..., 1]) - wh) 
+    iou = wh / union
+
+    centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
+    centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
+    centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
+    centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
+
+    inner_diag = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
+
+    xxc1 = np.minimum(bboxes1[..., 0], bboxes2[..., 0])
+    yyc1 = np.minimum(bboxes1[..., 1], bboxes2[..., 1])
+    xxc2 = np.maximum(bboxes1[..., 2], bboxes2[..., 2])
+    yyc2 = np.maximum(bboxes1[..., 3], bboxes2[..., 3])
+
+    outer_diag = (xxc2 - xxc1) ** 2 + (yyc2 - yyc1) ** 2
+    
+    w1 = bboxes1[..., 2] - bboxes1[..., 0]
+    h1 = bboxes1[..., 3] - bboxes1[..., 1]
+    w2 = bboxes2[..., 2] - bboxes2[..., 0]
+    h2 = bboxes2[..., 3] - bboxes2[..., 1]
+
+    # prevent dividing over zero. add one pixel shift
+    h2 = h2 + 1.
+    h1 = h1 + 1.
+    arctan = np.arctan(w2/h2) - np.arctan(w1/h1)
+    v = (4 / (np.pi ** 2)) * (arctan ** 2)
+    S = 1 - iou 
+    alpha = v / (S+v)
+    ciou = iou - inner_diag / outer_diag - alpha * v
+    
+    return (ciou + 1) / 2.0 # resize from (-1,1) to (0,1)
+
+
+def ct_dist(bboxes1, bboxes2):
+    """
+        Measure the center distance between two sets of bounding boxes,
+        this is a coarse implementation, we don't recommend using it only
+        for association, which can be unstable and sensitive to frame rate
+        and object speed.
+    """
+    bboxes2 = np.expand_dims(bboxes2, 0)
+    bboxes1 = np.expand_dims(bboxes1, 1)
+
+    centerx1 = (bboxes1[..., 0] + bboxes1[..., 2]) / 2.0
+    centery1 = (bboxes1[..., 1] + bboxes1[..., 3]) / 2.0
+    centerx2 = (bboxes2[..., 0] + bboxes2[..., 2]) / 2.0
+    centery2 = (bboxes2[..., 1] + bboxes2[..., 3]) / 2.0
+
+    ct_dist2 = (centerx1 - centerx2) ** 2 + (centery1 - centery2) ** 2
+
+    ct_dist = np.sqrt(ct_dist2)
+
+    # The linear rescaling is a naive version and needs more study
+    ct_dist = ct_dist / ct_dist.max()
+    return ct_dist.max() - ct_dist # resize to (0,1)
+
+
+
+def speed_direction_batch(dets, tracks):
+    tracks = tracks[..., np.newaxis]
+    CX1, CY1 = (dets[:,0] + dets[:,2])/2.0, (dets[:,1]+dets[:,3])/2.0
+    CX2, CY2 = (tracks[:,0] + tracks[:,2]) /2.0, (tracks[:,1]+tracks[:,3])/2.0
+    dx = CX1 - CX2 
+    dy = CY1 - CY2 
+    norm = np.sqrt(dx**2 + dy**2) + 1e-6
+    dx = dx / norm 
+    dy = dy / norm
+    return dy, dx # size: num_track x num_det
+
+
+def linear_assignment(cost_matrix):
+    try:
+        import lap
+        _, x, y = lap.lapjv(cost_matrix, extend_cost=True)
+        return np.array([[y[i],i] for i in x if i >= 0]) #
+    except ImportError:
+        from scipy.optimize import linear_sum_assignment
+        x, y = linear_sum_assignment(cost_matrix)
+        return np.array(list(zip(x, y)))
+
+
+def associate_detections_to_trackers(detections,trackers,iou_threshold = 0.3):
+    """
+    Assigns detections to tracked object (both represented as bounding boxes)
+    Returns 3 lists of matches, unmatched_detections and unmatched_trackers
+    """
+    if(len(trackers)==0):
+        return np.empty((0,2),dtype=int), np.arange(len(detections)), np.empty((0,5),dtype=int)
+
+    iou_matrix = iou_batch(detections, trackers)
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(-iou_matrix)
+    else:
+        matched_indices = np.empty(shape=(0,2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if(d not in matched_indices[:,0]):
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if(t not in matched_indices[:,1]):
+            unmatched_trackers.append(t)
+
+    #filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if(iou_matrix[m[0], m[1]]<iou_threshold):
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1,2))
+    if(len(matches)==0):
+        matches = np.empty((0,2),dtype=int)
+    else:
+        matches = np.concatenate(matches,axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+
+def associate(asso_func, detections, trackers, iou_threshold, velocities, previous_obs, vdc_weight):
+    if(len(trackers)==0):
+        return np.empty((0,2),dtype=int), np.arange(len(detections)), np.empty((0,5),dtype=int)
+
+    Y, X = speed_direction_batch(detections, previous_obs)
+    inertia_Y, inertia_X = velocities[:,0], velocities[:,1]
+    inertia_Y = np.repeat(inertia_Y[:, np.newaxis], Y.shape[1], axis=1)
+    inertia_X = np.repeat(inertia_X[:, np.newaxis], X.shape[1], axis=1)
+    diff_angle_cos = inertia_X * X + inertia_Y * Y
+    diff_angle_cos = np.clip(diff_angle_cos, a_min=-1, a_max=1)
+    diff_angle = np.arccos(diff_angle_cos)
+    diff_angle = (np.pi /2.0 - np.abs(diff_angle)) / np.pi
+
+    valid_mask = np.ones(previous_obs.shape[0])
+    valid_mask[np.where(previous_obs[:,4]<0)] = 0
+    
+    iou_matrix = asso_func(detections, trackers)
+    scores = np.repeat(detections[:,-1][:, np.newaxis], trackers.shape[0], axis=1)
+    # iou_matrix = iou_matrix * scores # a trick sometiems works, we don't encourage this
+    valid_mask = np.repeat(valid_mask[:, np.newaxis], X.shape[1], axis=1)
+
+    angle_diff_cost = (valid_mask * diff_angle) * vdc_weight
+    angle_diff_cost = angle_diff_cost.T
+    angle_diff_cost = angle_diff_cost * scores
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(-(iou_matrix+angle_diff_cost))
+    else:
+        matched_indices = np.empty(shape=(0,2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if(d not in matched_indices[:,0]):
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if(t not in matched_indices[:,1]):
+            unmatched_trackers.append(t)
+
+    # filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if(iou_matrix[m[0], m[1]]<iou_threshold):
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1,2))
+    if(len(matches)==0):
+        matches = np.empty((0,2),dtype=int)
+    else:
+        matches = np.concatenate(matches,axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
+
+
+def associate_kitti(detections, trackers, det_cates, iou_threshold, 
+        velocities, previous_obs, vdc_weight):
+    if(len(trackers)==0):
+        return np.empty((0,2),dtype=int), np.arange(len(detections)), np.empty((0,5),dtype=int)
+
+    """
+        Cost from the velocity direction consistency
+    """
+    Y, X = speed_direction_batch(detections, previous_obs)
+    inertia_Y, inertia_X = velocities[:,0], velocities[:,1]
+    inertia_Y = np.repeat(inertia_Y[:, np.newaxis], Y.shape[1], axis=1)
+    inertia_X = np.repeat(inertia_X[:, np.newaxis], X.shape[1], axis=1)
+    diff_angle_cos = inertia_X * X + inertia_Y * Y
+    diff_angle_cos = np.clip(diff_angle_cos, a_min=-1, a_max=1)
+    diff_angle = np.arccos(diff_angle_cos)
+    diff_angle = (np.pi /2.0 - np.abs(diff_angle)) / np.pi
+
+    valid_mask = np.ones(previous_obs.shape[0])
+    valid_mask[np.where(previous_obs[:,4]<0)]=0  
+    valid_mask = np.repeat(valid_mask[:, np.newaxis], X.shape[1], axis=1)
+
+    scores = np.repeat(detections[:,-1][:, np.newaxis], trackers.shape[0], axis=1)
+    angle_diff_cost = (valid_mask * diff_angle) * vdc_weight
+    angle_diff_cost = angle_diff_cost.T
+    angle_diff_cost = angle_diff_cost * scores
+
+    """
+        Cost from IoU
+    """
+    iou_matrix = iou_batch(detections, trackers)
+    
+
+    """
+        With multiple categories, generate the cost for catgory mismatch
+    """
+    num_dets = detections.shape[0]
+    num_trk = trackers.shape[0]
+    cate_matrix = np.zeros((num_dets, num_trk))
+    for i in range(num_dets):
+            for j in range(num_trk):
+                if det_cates[i] != trackers[j, 4]:
+                        cate_matrix[i][j] = -1e6
+    
+    cost_matrix = - iou_matrix -angle_diff_cost - cate_matrix
+
+    if min(iou_matrix.shape) > 0:
+        a = (iou_matrix > iou_threshold).astype(np.int32)
+        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
+            matched_indices = np.stack(np.where(a), axis=1)
+        else:
+            matched_indices = linear_assignment(cost_matrix)
+    else:
+        matched_indices = np.empty(shape=(0,2))
+
+    unmatched_detections = []
+    for d, det in enumerate(detections):
+        if(d not in matched_indices[:,0]):
+            unmatched_detections.append(d)
+    unmatched_trackers = []
+    for t, trk in enumerate(trackers):
+        if(t not in matched_indices[:,1]):
+            unmatched_trackers.append(t)
+
+    #filter out matched with low IOU
+    matches = []
+    for m in matched_indices:
+        if(iou_matrix[m[0], m[1]]<iou_threshold):
+            unmatched_detections.append(m[0])
+            unmatched_trackers.append(m[1])
+        else:
+            matches.append(m.reshape(1,2))
+    if(len(matches)==0):
+        matches = np.empty((0,2),dtype=int)
+    else:
+        matches = np.concatenate(matches,axis=0)
+
+    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)
\ No newline at end of file
diff --git a/trackers/ocsort/cmc.py b/trackers/ocsort/cmc.py
new file mode 100644
index 0000000000000000000000000000000000000000..333a417ce299d79a92a765eb1fe30d936f50a542
--- /dev/null
+++ b/trackers/ocsort/cmc.py
@@ -0,0 +1,343 @@
+import cv2
+import matplotlib.pyplot as plt
+import numpy as np
+import copy
+import time
+
+
+class GMC:
+    def __init__(self, method='cmc', downscale=2, verbose=None):
+        super(GMC, self).__init__()
+
+        self.method = method
+        self.downscale = max(1, int(downscale))
+
+        if self.method == 'orb':
+            self.detector = cv2.FastFeatureDetector_create(20)
+            self.extractor = cv2.ORB_create()
+            self.matcher = cv2.BFMatcher(cv2.NORM_HAMMING)
+
+        elif self.method == 'sift':
+            self.detector = cv2.SIFT_create(nOctaveLayers=3, contrastThreshold=0.02, edgeThreshold=20)
+            self.extractor = cv2.SIFT_create(nOctaveLayers=3, contrastThreshold=0.02, edgeThreshold=20)
+            self.matcher = cv2.BFMatcher(cv2.NORM_L2)
+
+        elif self.method == 'ecc':
+            number_of_iterations = 5000
+            termination_eps = 1e-6
+            self.warp_mode = cv2.MOTION_EUCLIDEAN
+            self.criteria = (cv2.TERM_CRITERIA_EPS | cv2.TERM_CRITERIA_COUNT, number_of_iterations, termination_eps)
+
+        elif self.method == 'sparseOptFlow':
+            self.feature_params = dict(maxCorners=1000, qualityLevel=0.01, minDistance=1, blockSize=3,
+                                       useHarrisDetector=False, k=0.04)
+            # self.gmc_file = open('GMC_results.txt', 'w')
+
+        elif self.method == 'cmc':
+            self.prev_gray = None
+            # self.gmcFile = open("./GMC-11-2.txt", 'r')
+        elif self.method == 'none' or self.method == 'None':
+            self.method = 'none'
+        else:
+            raise ValueError("Error: Unknown CMC method:" + method)
+
+        self.prevFrame = None
+        self.prevKeyPoints = None
+        self.prevDescriptors = None
+
+        self.initializedFirstFrame = False
+
+    def apply(self, raw_frame, detections=None):
+        if self.method == 'orb' or self.method == 'sift':
+            return self.applyFeaures(raw_frame, detections)
+        elif self.method == 'ecc':
+            return self.applyEcc(raw_frame, detections)
+        elif self.method == 'sparseOptFlow':
+            return self.applySparseOptFlow(raw_frame, detections)
+        elif self.method == 'cmc':
+            return self.applyFile(raw_frame, detections)
+        elif self.method == 'none':
+            return np.eye(2, 3)
+        else:
+            return np.eye(2, 3)
+
+    def applyEcc(self, raw_frame, detections=None):
+
+        # Initialize
+        height, width, _ = raw_frame.shape
+        frame = cv2.cvtColor(raw_frame, cv2.COLOR_BGR2GRAY)
+        H = np.eye(2, 3, dtype=np.float32)
+
+        # Downscale image (TODO: consider using pyramids)
+        if self.downscale > 1.0:
+            frame = cv2.GaussianBlur(frame, (3, 3), 1.5)
+            frame = cv2.resize(frame, (width // self.downscale, height // self.downscale))
+            width = width // self.downscale
+            height = height // self.downscale
+
+        # Handle first frame
+        if not self.initializedFirstFrame:
+            # Initialize data
+            self.prevFrame = frame.copy()
+
+            # Initialization done
+            self.initializedFirstFrame = True
+
+            return H
+
+        # Run the ECC algorithm. The results are stored in warp_matrix.
+        # (cc, H) = cv2.findTransformECC(self.prevFrame, frame, H, self.warp_mode, self.criteria)
+        try:
+            (cc, H) = cv2.findTransformECC(self.prevFrame, frame, H, self.warp_mode, self.criteria, None, 1)
+        except:
+            print('Warning: find transform failed. Set warp as identity')
+
+        return H
+
+    def applyFeaures(self, raw_frame, detections=None):
+
+        # Initialize
+        height, width, _ = raw_frame.shape
+        frame = cv2.cvtColor(raw_frame, cv2.COLOR_BGR2GRAY)
+        H = np.eye(2, 3)
+
+        # Downscale image (TODO: consider using pyramids)
+        if self.downscale > 1.0:
+            # frame = cv2.GaussianBlur(frame, (3, 3), 1.5)
+            frame = cv2.resize(frame, (width // self.downscale, height // self.downscale))
+            width = width // self.downscale
+            height = height // self.downscale
+
+        # find the keypoints
+        mask = np.zeros_like(frame)
+        # mask[int(0.05 * height): int(0.95 * height), int(0.05 * width): int(0.95 * width)] = 255
+        mask[int(0.02 * height): int(0.98 * height), int(0.02 * width): int(0.98 * width)] = 255
+        if detections is not None:
+            for det in detections:
+                tlbr = (det[:4] / self.downscale).astype(np.int_)
+                mask[tlbr[1]:tlbr[3], tlbr[0]:tlbr[2]] = 0
+
+        keypoints = self.detector.detect(frame, mask)
+
+        # compute the descriptors
+        keypoints, descriptors = self.extractor.compute(frame, keypoints)
+
+        # Handle first frame
+        if not self.initializedFirstFrame:
+            # Initialize data
+            self.prevFrame = frame.copy()
+            self.prevKeyPoints = copy.copy(keypoints)
+            self.prevDescriptors = copy.copy(descriptors)
+
+            # Initialization done
+            self.initializedFirstFrame = True
+
+            return H
+
+        # Match descriptors.
+        knnMatches = self.matcher.knnMatch(self.prevDescriptors, descriptors, 2)
+
+        # Filtered matches based on smallest spatial distance
+        matches = []
+        spatialDistances = []
+
+        maxSpatialDistance = 0.25 * np.array([width, height])
+
+        # Handle empty matches case
+        if len(knnMatches) == 0:
+            # Store to next iteration
+            self.prevFrame = frame.copy()
+            self.prevKeyPoints = copy.copy(keypoints)
+            self.prevDescriptors = copy.copy(descriptors)
+
+            return H
+
+        for m, n in knnMatches:
+            if m.distance < 0.9 * n.distance:
+                prevKeyPointLocation = self.prevKeyPoints[m.queryIdx].pt
+                currKeyPointLocation = keypoints[m.trainIdx].pt
+
+                spatialDistance = (prevKeyPointLocation[0] - currKeyPointLocation[0],
+                                   prevKeyPointLocation[1] - currKeyPointLocation[1])
+
+                if (np.abs(spatialDistance[0]) < maxSpatialDistance[0]) and \
+                        (np.abs(spatialDistance[1]) < maxSpatialDistance[1]):
+                    spatialDistances.append(spatialDistance)
+                    matches.append(m)
+
+        meanSpatialDistances = np.mean(spatialDistances, 0)
+        stdSpatialDistances = np.std(spatialDistances, 0)
+
+        inliesrs = (spatialDistances - meanSpatialDistances) < 2.5 * stdSpatialDistances
+
+        goodMatches = []
+        prevPoints = []
+        currPoints = []
+        for i in range(len(matches)):
+            if inliesrs[i, 0] and inliesrs[i, 1]:
+                goodMatches.append(matches[i])
+                prevPoints.append(self.prevKeyPoints[matches[i].queryIdx].pt)
+                currPoints.append(keypoints[matches[i].trainIdx].pt)
+
+        prevPoints = np.array(prevPoints)
+        currPoints = np.array(currPoints)
+
+        # Draw the keypoint matches on the output image
+        if 0:
+            matches_img = np.hstack((self.prevFrame, frame))
+            matches_img = cv2.cvtColor(matches_img, cv2.COLOR_GRAY2BGR)
+            W = np.size(self.prevFrame, 1)
+            for m in goodMatches:
+                prev_pt = np.array(self.prevKeyPoints[m.queryIdx].pt, dtype=np.int_)
+                curr_pt = np.array(keypoints[m.trainIdx].pt, dtype=np.int_)
+                curr_pt[0] += W
+                color = np.random.randint(0, 255, (3,))
+                color = (int(color[0]), int(color[1]), int(color[2]))
+
+                matches_img = cv2.line(matches_img, prev_pt, curr_pt, tuple(color), 1, cv2.LINE_AA)
+                matches_img = cv2.circle(matches_img, prev_pt, 2, tuple(color), -1)
+                matches_img = cv2.circle(matches_img, curr_pt, 2, tuple(color), -1)
+
+            plt.figure()
+            plt.imshow(matches_img)
+            plt.show()
+
+        # Find rigid matrix
+        if (np.size(prevPoints, 0) > 4) and (np.size(prevPoints, 0) == np.size(prevPoints, 0)):
+            H, inliesrs = cv2.estimateAffinePartial2D(prevPoints, currPoints, cv2.RANSAC)
+
+            # Handle downscale
+            if self.downscale > 1.0:
+                H[0, 2] *= self.downscale
+                H[1, 2] *= self.downscale
+        else:
+            print('Warning: not enough matching points')
+
+        # Store to next iteration
+        self.prevFrame = frame.copy()
+        self.prevKeyPoints = copy.copy(keypoints)
+        self.prevDescriptors = copy.copy(descriptors)
+
+        return H
+
+    def applySparseOptFlow(self, raw_frame, detections=None):
+
+        t0 = time.time()
+
+        # Initialize
+        height, width, _ = raw_frame.shape
+        frame = cv2.cvtColor(raw_frame, cv2.COLOR_BGR2GRAY)
+        H = np.eye(2, 3)
+
+        # Downscale image
+        if self.downscale > 1.0:
+            # frame = cv2.GaussianBlur(frame, (3, 3), 1.5)
+            frame = cv2.resize(frame, (width // self.downscale, height // self.downscale))
+
+        # find the keypoints
+        keypoints = cv2.goodFeaturesToTrack(frame, mask=None, **self.feature_params)
+
+        # Handle first frame
+        if not self.initializedFirstFrame:
+            # Initialize data
+            self.prevFrame = frame.copy()
+            self.prevKeyPoints = copy.copy(keypoints)
+
+            # Initialization done
+            self.initializedFirstFrame = True
+
+            return H
+
+        # find correspondences
+        matchedKeypoints, status, err = cv2.calcOpticalFlowPyrLK(self.prevFrame, frame, self.prevKeyPoints, None)
+
+        # leave good correspondences only
+        prevPoints = []
+        currPoints = []
+
+        for i in range(len(status)):
+            if status[i]:
+                prevPoints.append(self.prevKeyPoints[i])
+                currPoints.append(matchedKeypoints[i])
+
+        prevPoints = np.array(prevPoints)
+        currPoints = np.array(currPoints)
+
+        # Find rigid matrix
+        if (np.size(prevPoints, 0) > 4) and (np.size(prevPoints, 0) == np.size(prevPoints, 0)):
+            H, inliesrs = cv2.estimateAffinePartial2D(prevPoints, currPoints, cv2.RANSAC)
+
+            # Handle downscale
+            if self.downscale > 1.0:
+                H[0, 2] *= self.downscale
+                H[1, 2] *= self.downscale
+        else:
+            print('Warning: not enough matching points')
+
+        # Store to next iteration
+        self.prevFrame = frame.copy()
+        self.prevKeyPoints = copy.copy(keypoints)
+
+        t1 = time.time()
+
+        # gmc_line = str(1000 * (t1 - t0)) + "\t" + str(H[0, 0]) + "\t" + str(H[0, 1]) + "\t" + str(
+        #     H[0, 2]) + "\t" + str(H[1, 0]) + "\t" + str(H[1, 1]) + "\t" + str(H[1, 2]) + "\n"
+        # self.gmc_file.write(gmc_line)
+
+        return H
+
+    def applyFile(self, raw_frame, detections=None):
+        line = self.gmcFile.readline()
+        tokens = line.split("\t")
+        H = np.eye(2, 3, dtype=np.float_)
+        H[0, 0] = float(tokens[1])
+        H[0, 1] = float(tokens[2])
+        H[0, 2] = float(tokens[3])
+        H[1, 0] = float(tokens[4])
+        H[1, 1] = float(tokens[5])
+        H[1, 2] = float(tokens[6])
+
+        return H
+
+    def applyCMC(self, frame):
+        # Convert frame to grayscale
+        curr_gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
+
+        # Handle first frame
+        if not self.initializedFirstFrame:
+            # Initialization
+            self.initializedFirstFrame = True
+            self.prev_gray = np.copy(curr_gray)
+            return np.eye(2, 3, dtype=np.float32)  # Return identity matrix for the first frame
+
+        # Detect feature points in previous frame
+        prev_pts = cv2.goodFeaturesToTrack(self.prev_gray, maxCorners=200, qualityLevel=0.01, minDistance=30,
+                                           blockSize=3)
+        # Calculate optical flow (i.e. track feature points)
+        curr_pts, status, err = cv2.calcOpticalFlowPyrLK(self.prev_gray, curr_gray, prev_pts, None)
+
+        if curr_pts is None:
+            return np.eye(2, 3)  # Return identity matrix if no good points are found
+
+        # Sanity check
+        assert prev_pts.shape == curr_pts.shape
+        # Filter only valid points
+        idx = np.where(status == 1)[0]
+        prev_pts = prev_pts[idx]
+        curr_pts = curr_pts[idx]
+        # Find transformation matrix
+        # m, inliers = cv2.estimateAffinePartial2D(prev_pts, curr_pts)
+        m, inliers = cv2.estimateAffine2D(prev_pts, curr_pts)
+        # Update the previous frame and points
+        self.prev_gray = np.copy(curr_gray)
+
+        # Determine camera movement
+        translation_magnitude = np.sqrt(m[0, 2] ** 2 + m[1, 2] ** 2)
+        scaling_factor = np.linalg.det(m[:, :2])
+
+        # Check if camera has moved based on thresholds
+        if translation_magnitude < 1.0 and abs(scaling_factor - 1) < 0.1:
+            # print("No significant camera movement")
+            return np.eye(2, 3)
+
+        return m if m is not None else np.eye(2, 3)  # If estimation fails, return identity matrix