Global Positioning System Reference
In-Depth Information
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[31
Lin
—
1
——
No
PgE
Figure 8.4
Geoid undulations with respect to the local ellipsoid.
Units are in centimeters.
[31
)
and a scale factor
implied by model (8.27). There are seven minimal constraints required in this case,
e.g., the geodetic latitude and longitude for two stations and the geodetic heights
for three stations distributed well over the network. If one uses orthometric heights
for these three stations instead, the angles
(
Alternatively, one can estimate the topocentric rotations
(
η
,
ξ
,
α
)
reflect the average deflection of
the vertical angles. Using orthometric heights instead of geodetic heights forces the
ellipsoid to coincide locally with the geoid (as defined or implied by the orthometric
heights at the vertical stations). The rotation in azimuth
ξ
,
η
is determined by the
azimuthal difference between the two stations held fixed and the GPS vector between
the same stations. The scale factor is also determined by the two stations held fixed;
it contains the possible scale error of the existing geodetic network and the effect of a
constant but unknown undulation (i.e., geoid undulations with respect to the ellipsoid
of the existing geodetic network).
Simple geometric interpolation of geoid undulations has its limits, of course. For
example, any error in a given orthometric height will result inevitably in an erroneous
geoid feature. As a result, the orthometric heights computed from the interpolated
geoid undulations will be in error. Depending on the size of the survey area and the
“smoothness” of the geoid in that region, such erroneous geoid features might or
might not be discovered from data analysis. These difficulties can be avoided if an
accurate geoid model is available.
α
