29
d. Analysis of the Accuracy of the Spatial Triangulation
From the average values in the foregoing tabulation, one
can derive a theoretical mean error of the spatial triangula
tion procedure. Accuracy studies made in connection with the
SAO catalog lead to the conclusion that the star field as a
whole will not allow a statistical improvement below the ±0"2
or ±0.5 micron level, even that being, at present, some what
optimistic relative to southern hemisphere stars. Applying
the square root law, the uncertainty in the photogrammetrie
bundle reconstruction should be reduced, using an average of
seven hundred star images, by a factor of 7*5? at least for
the area at the center of the plate, resulting consequently
in ±2.97/7-5 - ±0.4 microns random error contribution. Using
an average of 308 satellite images per plate, the precision of
a point interpolated near the center of the plate into the
polynomial curve fit equation should be better by a factor
of eight, compared to the average mean error of the curve
fits. Consequently, the fictitious satellite position should
contribute ±3.08/8 = ±0.4 microns. The total random noise in 1
the triangulation must then be expected to be (0. 5 2+ 0. 4 2 + 0.4 2 ) s’
= ±0.8 micron. The least squares adjustments of the spatial
triangulation have,typically, mean errors for a single observed
direction of ±1.05 to ±1.06 microns. The last such adjust
ment (lj June 1968) included 25 stations, 1534 observations, 1128
unknowns and, consequently, 4o6 degrees of freedom. Three-
hundred forty-nine satellite passes were used. Figure 12
shows the distribution of the plate residuals of the most
recent adjustment. The area under the normal curve equals
the area under the histogram. These data indicate the
presence of a slight systematic error source, as does the fact
that the mean error of ±1.05 microns is larger than the
expected mean error of ±0.8 micron. Presently, three sources
of small systematic errors are known to exist. First,
Universal Time (UT-l) furnished during the observational
period was not a true measure of earth rotation. The neces
sary additional corrections have now been obtained and will
be applied. Secondly, and probably most important, the
present reduction of the single cameras uses only a mean
between the orientations before and after the satellite
passage. The presently developed reduction techniques allow
the elimination of any field instrumentation instability.
Finally, the present reductions fail to take into account
the difference of amount of earth rotation due to the dif
ference in light travel time between satellite and observing
stations. In order to produce a final result as free as
possible from systematic error sources, we have decided to