4.
of height differences on the adjusted X,Y, and Z coordinates. Let me emphasize
that all geodetic points were used in the adjustment, so that the adjustment curve
of true best fit was obtained for each triangulation. The standard residual errors
for the triangulations are listed in Table 1.
Table 1
Standard Errors of Triangulation Points After Adjustment
m x
my
m z
Triangulation 1, 36 models
±2.6 m.
±2.7 m.
±2.8 m.
h 2 m m
1.8
1.9
CO
3, " " , aerial levelling
2.1
2.1
to
00
" 4, 9
1.3
1.5
00
rH
" 5, "
1.1
1.3
1.5
Analytical triangulation, 30 models
2.8
3.1
6.4
Fictitious triangulation 2, 36 models
1.7
1.9
00
CO
The poor results of the analytical triangulation are a direct consequence of using
weak configurations of relative orientation points.
Figure 8 shows the individual residual errors for fictitious and actual triangu
lation 2. Note that there are no "breaks" in the residual errors. None of the
other triangulations showed any breaks. This was unfortunate, as I had planned
to examine the effect of orientation errors in producing these breaks.
In Figure 8, remember that the fictitious triangulation 2 contains only errors
made in the orientation elements. The actual triangulation 2 has all the error
causes found in aerial triangulation, except film shrinkage. Yet the two sets of
residuals show a very close resemblance. This indicates the great importance of
orientation errors on the final residual coordinate errors of a triangulation.
Conclusions - This empirical study leads to several conclusions. I realize that
work with one strip of photographs on one particular instrument is rather limited
grounds for definite conclusions. I would like to see this sort of study performed
by others with other instruments and photography so that results can be compared.
This empirical study indicates that:
1. Successive orientation element errors fluctuate greatly, and do not
propagate smoothly from photograph to photograph ;
2. There is a great similarity in the pattern of these consecutive fluctu
ations for several triangulations of the same strip, even when the triangulations
are performed by different methods and using different points for orientation;
3. The orientation errors are correlated so that the strip coordinate errors
of triangulation points propagate much more smoothly than the errors of orientation.
This is well known. However, the strip coordinates still deviate slightly from
third degree polynomials. It appears that the deviations caused only by orienta
tion errors are very similar in value and strip location to the residual errors from
all causes. This indicates that orientation errors are the single most important
aause of the residual errors of points determined by aerial strip triangulation ,
at least when using glass plate photography.
The extensive analytical work performed in this research was all performed
with the Control Data 160A digital computer of the Arecibo Ionospheric Observa
tory, operated by Cornell University under contract to the United States Air
Force Office of Scientific Research.