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 
ito] # 
Hu 
“ 
4 
1 
10.0 5 i 
my[m] = Ky fr M-107 / 
my[m) = Ky-u-M-107° / 
s munie Ky ue 4 
y = mean square error of unit weight in microns / 
M-É (scalefactor) / 
8.0 A 
70 
6.0 
50 / 
40 
  
  
  
  
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 
myIml-K, uM 1078 
mylmi-K y uM 108 
M 
H 
  
  
    
     
min" max (scalefactor) 
max(for 90° cone)- 2; s-length of strip 
  
  
x N 
05 | NE “a 
tes med 2 Zs 
NUUS AU et Ee enema mamme d n. 
Tate ee ES Ys. —- 
Zst 
Yst 
[9] 
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 
spe 
pro 
an c 
dist: 
it is | 
of p 
corre