Global Positioning System Reference
In-Depth Information
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TABLE 8.2
Design Submatrix for the Transformation Parameters
s
η
ξ
α
u
m
−
u
k
M
(
u
m
−
u
k
)
M
ξ
(
u
m
−
u
k
)
M
α
(
u
m
−
u
k
)
η
coordinates for (a) Cartesian parameterization, (b) parameterization in terms of geo-
detic latitude, longitude, and height, and (c) parameterization in terms of the local
geodetic coordinate systems. The transformation matrices
J
and
H
referred to in the
table are those of (2.106) and (2.108). Table 8.2 contains the partial derivatives of the
transformation parameters.
[30
8.4 GPS NETWORK EXAMPLES
In these examples only independent vectors between stations are included; i.e., if
three receivers observe simultaneously, only two vectors are used. The stochastic
model does not include the mathematical correlation between simultaneously ob-
served vectors. The variance-covariance matrix of the observed vectors is 3
Lin
—
-0.
——
Nor
PgE
×
3
block-diagonal. Craymer and Beck (1992) discuss various aspects of session ver-
sus single-baseline processing. They also point out that inclusion of the trivial (de-
pendent) baselines distorts the formal accuracy by increasing the redundancy in the
model artificially, resulting in overly optimistic covariance matrices. The covariance
information used was obtained directly from baseline processing and does not accom-
modate small uncertainties in eccentricity, i.e., setting up the antenna over the mark.
Only single-frequency carrier phases were available at the time the observations were
made.
[30
8.
4.1 Montgomery County Geodetic Network
At the time of the Montgomery County (Pennsylvania) geodetic network densifica-
tion, the window of satellite visibility was about 5 hours for GPS, just long enough to
allow two sessions with the then state-of-the-art static approach (Collins and Leick,
1985). Much liberty was taken in the network design (Figure 8.2) by taking advan-
tage of GPS's insensitivity to the shape of the network (as compared to the many
rules of classical triangulation and trilateration). The longest baseline observed was
about 42 km. Six horizontal stations with known geodetic latitude and longitude and
seven vertical stations with known orthometric height were available for tying the
GPS survey to the existing geodetic networks. Accurate geoid information was not
available at the time.
Figure 8.3 shows two intersections of the ellipsoid of standard deviation for the
inner constraint least-squares solution. The top set of ellipses shows the horizontal
intersection (i.e., the ellipses of standard deviation in the geodetic horizon), and the
bottom set of ellipses shows the vertical intersection in the east-west direction. The
figure also shows the daily satellite visibility plot for the time and area of the project.
