INTRODUCTION - GPS Satellite Surveying - page 3

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observable. It can be readily shown that single differences are largely independent of
satellite frequency offset and linear drift. Next, assume that two single differences are
available, one referring to satellite p and one to satellite q . The difference between
these two single differences, called the double-difference observable, is largely inde-
pendent of receiver clock errors. Finally, taking the difference of two double differ-
ences that refer to different epochs yields the triple-difference observable. This last
type of observation is useful for initial processing and screening of the data.
Single-, double-, or triple-difference processing yields the relative location be-
tween the co-observing receivers and is usually referred to as the vector between the
stations. Because the satellites are at a finite distance from the earth, there is also
a “geocentric positioning component” to these observables which is, as a matter of
fact, a function of the baseline length. In practice, the absolute location of the baseline
must be sufficiently known in order not to degrade the relative positioning capability.
This topic will be discussed later. By itself, one accurate vector between stations is
generally not of much use, at least in surveying. Of course, one can add the vector to
the geocentric position of the “known” station and formally compute the geocentric
position of the new station. The problem with this procedure is that the uncertainty of
the “known” station is transferred in full to the new station. Also, despite all of modern
technology, the vectors themselves can still be in error. Possibilities of misidentify-
ing ground marks, centering errors, misreading antenna heights, etc., can never be
completely avoided. Like other observations, the GPS vector observations are most
effectively controlled by a least-squares network adjustment consisting of a set of
redundant vectors. Such network solutions make it possible to assess the quality of
the observations, validate the correctness of statistical data, and detect (and possi-
bly remove) existing blunders. Therefore, the primary result of a GPS survey is a
polyhedron of stations whose accurate relative locations have been controlled by a
least-squares adjustment.

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1.1 HISTORICAL PERSPECTIVE

A summary of GPS development and performance to date is detailed in Table 1.1.
Because the scope of GPS research and application development is so broad and
conducted by researchers all over the globe, it is impossible to give a comprehensive
listing. Table 1.1, therefore, merely demonstrates the extraordinarily rapid develop-
ment of the GPS positioning system.
GPS made its debut in surveying and geodesy with a big bang. During the summer
of 1982, the testing of the Macrometer receiver, developed by C. C. Counselman at
M.I.T., verified a GPS surveying accuracy of 1-2 parts per million (ppm) of the station
separation. Baselines were measured repeatedly using several hours of observations
to study this new surveying technique and to gain initial experience with GPS. Dur-
ing 1983 a thirty (plus)-station first-order network densification in the Eifel region
of Germany was observed (Bock et al., 1985). This project was a joint effort by the
State Surveying Office of North Rhein-Westfalia, a private U.S. firm, and scientists
from M.I.T. In early 1984, the geodetic network densification of Montgomery County
(Pennsylvania) was completed. The sole guidance of this project rested with a private