11
FACTORS FOR ELLIPSOID HEIGHT, LATITUDE. AND LONGITUDE USING I TO 4 SCALARS
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necessary ties and astronomical observations. The scalers
are established by three-dimensional traverses with distances
being measured by Geodimeter or electronic distance measur
ing equipment. In combination with astronomical observations
and precise angle measurements it is expected that these
traverses provide the chord distances between pairs of sta
tions in the world net to one part in one million.
The need for these scalers is demonstrated by theoretical
studies of the error propagation in photogrammetric satellite
triangulation. In Figure 3 it is shown that, typically, the
longest axes of the error ellipsoids are normal to the earth's
surface. When considering two stations diametrically opposed
to each other, these error components represent the uncertainty
in scale of the world net. Consequently, additional scale
lines provide the necessary information in order to reduce
these errors. The situation is shown in Figure 4, in the
upper portion of which the improvement in accuracy of the
height component is shown as the number of measured scalers
increases. Denoting the more or less equal amounts of the
mean errors in latitude and longitude, as shown in the lower
portion of Figure 4, by unity it can be seen that the mean
error in the direction of height is roughly three when only
one scaler is introduced. With four scalers these mean errors
are reduced to 1.8. It is, therefore, reasonable to expect
as the ultimate accuracy with the PAGEOS satellite, posi
tional mean errors f*or the latitude and longitude components
of ±6 meter, and +11 meter in the direction of height.
Figure 5 shows the axes of the error ellipsoids for 25
stations as obtained from the adjustment of the presently
reduced data. The results are obtained from 730 photo
graphs, representing about 33% of the ultimately expected
raw data. Because the 25 incorporated stations represent
about 55% of all stations it is obvious that the result of
this adjustment still suffers from a deficiency of informa
tion; this accounts for the larger mean errors. However,
in areas where all of the necessary measurements have been
obtained and reduced, the corresponding mean errors, indexed
by are in reassuring agreement with theoretical expecta
tions, particularly since only one scaler was used.
A comparison of the results obtained so far with classic
geodetic data and with results obtained by other systems of
satellite geodesy, especially the results from dynamic geodesy,
already provide interesting information, the value of which
can be expected to increase qualitatively and quantitatively
with the progress of the program. Such consideration would