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CHAPTER 1
INTRODUCTION
1.1 INTRODUCTION
We currently live in what is often termed the information age. Aided by new
and emerging technologies, data are being collected at unprecedented rates in all
walks of life. For example, in the field of surveying, total station instruments,
global navigation satellite systems (GNSS), digital metric cameras, laser-scanning
systems, and satellite imaging systems are only some of the new instruments that
are now available for rapid generation of vast quantities of observed data.
Geographic information systems (GIS) have evolved concurrently with the
development of these new data acquisition instruments. GIS are now used exten sively for management, planning, and design. They are being applied worldwide
at all levels of government, in business and industry, by public utilities, and in
private engineering and surveying offices. Implementation of a GIS depends on
large quantities of data from a variety of sources, many of them consisting of
observations made with the new instruments, such as those noted above.
However, before data can be utilized, whether for surveying and mapping
projects, for engineering design, or for use in a geographic information sys tem, they must be processed. One of the most important aspects of this is to
account for the fact that no measurements are exact; that is, they always contain
errors.
The steps involved in accounting for the existence of errors in observations
consist of (1) performing statistical analyses of the observations to assess the
magnitudes of their errors and to study their distributions to determine whether or
not they are within acceptable tolerances; and if the observations are acceptable,
(2) adjusting them so that they conform to exact geometric conditions or other
Adjustment Computations: Spatial Data Analysis, Fifth Edition, Charles D. Ghilani
2010 by John Wiley & Sons, Inc. Published by John Wiley & Sons, Inc.
1
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2 INTRODUCTION
required constraints. Procedures for performing these two steps in processing
measured data are principal subjects of this book.
1.2 DIRECT AND INDIRECT MEASUREMENTS
Measurements are defined as observations made to determine unknown quantities.
They may be classified as either direct or indirect. Direct measurements are
made by applying an instrument directly to the unknown quantity and observing
its value, usually by reading it directly from graduated scales on the device.
Determining the distance between two points by making a direct measurement
using a graduated tape, or measuring an angle by making a direct observation
from the graduated circle of a total station instrument, are examples of direct
measurements.
Indirect measurements are obtained when it is not possible or practical to
make direct measurements. In such cases the quantity desired is determined from
its mathematical relationship to direct measurements. For example, surveyors
may observe angles and lengths of lines between points directly and use these
observations to compute station coordinates. From these coordinate values, other
distances and angles that were not observed directly may be derived indirectly
by computation. During this procedure, the errors that were present in the origi nal direct observations are propagated (distributed) by the computational process
into the indirect values. Thus, the indirect measurements (computed station coor dinates, distances, and angles) contain errors that are functions of the original
errors. This distribution of errors is known as error propagation. The analysis of
how errors propagate is also a principal topic of this book.
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