22 ANALYTICAL AERIAL TRIANGULATION, DISCUSSION
very complex system, for instance, block trian-
gulation or special multi-ray-triangulation,
which will probably become in the future a
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5 7 9 M 13 IS 17 19 21 23
No. of photographs in the strip
Fig. 2
requirement for satellite orbital determinations
for which photogrammetry may be the only
solution. It seems to me that the whole photo-
grammetric approach can be based on a far
more simple answer if you realise that each
photograph which we take is an individual one
and is entirely self-sustained. In other words,
taking our photogram does not need to know
that we intend to photograph the object again
from other stations. Consequently, it should be
possible to derive a condition equation which
only contains the geometrical properties of the
individual bundle.
Obviously, such a condition is that three
points are situated on a straight line. The object
point, the centre of projection and the image
point. This simple model is not only flexible but
physical disturbances, like reflection on one side
and distortion on the other side, can easily be
applied as perturbations to this co-linearity
condition, but this leads to simple straightfor-
ward observations and correspondingly to a
normal equation system.
This method has been programmed for
electronic computing and lately we have suc-
ceeded with the strip. In the last few months we
were able to invert quite large matrices — up to
54 photographs, which means thousands of
unknowns.
I have a few slides which I would like to
show you. I have used fictitious photography
to study first such strips, because results seem
to indicate that analytical photogrammetry is
confronted with serious obstacles.
It is of interest to study the maximum errors
in the center of a strip in relation to its length.
Fig. 1 shows the corresponding information for
the orientation elements of the camera stations
for each center photograph of strips varying in
length from 5 to 54 photographs. Although the
accumulation of the errors of the rotational
parameters increases with the length of the strip,
it is seen that the corresponding laws of error
propagation are not unfavorable. However, the
corresponding curves for the positional para-
meters (denoted by X, Y, Z,) show the un-
favorable effect of the double summation of
errors.
Fig. 2 provides the corresponding informa-
tion for points on the ground. The result is
plotted for strips varying in length from 5 to 23
photographs. The heavy lines refer to a point in
the middle of the strip, while the thin lines show
the corresponding results for a point situated
at the edge of the strip. It is evident that the
error accumulation for all three coordinates is
unfavorably influenced by the double summa-
tion of errors. All results are obtained from a
rigorous least squares adjustment treating the
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T T T T T T T T T T T T T T T T T T T
5 7 9 11 13 15 17 19 21 23
No of photographs in the strip of con-
stant length
Fig. 3
whole strip simultaneously. Furthermore, the
idealizing assumption was made that only
normally distributed errors are present. There-
for
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