Global Positioning System Reference
In-Depth Information
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important point in favor of the three-dimensional model is that the geodesic line on
the ellipsoid is not needed at all. Anyone who has studied the mathematics related to
geodesics will certainly appreciate this simplification of surveying theory.
The 3D geodetic model requires that the observations are reduced for polar mo-
tion and deflection of the vertical. It is well known that the theodolite senses the
local plumb line and, thus, measures with respect to the local vertical and the local
astronomic horizon. It is further known that astronomic observations depend on the
position of the instantaneous pole of rotation. The goal is to reduce angular obser-
vations measured with the theodolite to the ellipsoidal normal (deflection of vertical
reduction) and to reduce the astronomic quantities to the conventional terrestrial pole
(CTP). Having said this, I would like to comfort worried surveyors by reminding
them that the most popular observations do not depend critically on polar motion and
deflection of the vertical; e.g., horizontal angles depend very little on the deflection
of the vertical (because horizontal angles are the difference between two azimuths,
the largest deflection term cancels). The GPS vector observations (which refer to a
crust-fixed coordinate system, whose third axis coincides with the CTP) and distances
measured with the electronic distance meter (EDM) do not depend on either polar
motion or deflection of the vertical. Furthermore, modern surveyors are unlikely to
make astronomic observations in view of GPS surveying capability.
In surveying applications, there will typically be no need to improve on the de-
flection of the vertical already available from, e.g., the NGS. Besides, surveyors can
[9]
Lin
—
1
——
No
PgE
[9]
reduction
to
mapping
plane
mapping plane
to
ellipsoid
conformal
mapping plane
model
reduction
to
ellipsoid
ellipsoidal
surface
model
ellipsoid
to
3D
polar motion
and
deflection
correction
deflection
of the
vertical
3D geodetic
model
controlled
observations
original
observations
Figure 1.1
Geodetic models.
