International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
After the visual evaluation of the tie points the accuracy of the 
ray intersections was analysed. First, the values of the exterior 
orientation from ESA have been fixed in the bundle adjustment 
and no DTM as control information has been introduced. This 
can be considered as a forward intersection. In Table 1 the 
theoretical standard deviations of the object coordinates of the 
ray intersections are shown for the selected orbits. Only 3-fold 
points have been used for all computations. 
orientation like in Table 1. As expected the accuracy of the tie 
points increases from level to level. Table 5 shows the standard 
deviations after the bundle adjustment. It can be seen that on 
each level the standard deviation can be improved by a factor of 
about 2 and the best results are achieved on the original level. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
orbit | altitude [km] oX [m] cY [m] oZ [m] 
18 275 — 347 12.9 11.0 34.3 
22 311 —941 132 18.1 42.2 
68 269 — 505 30.3 27.6 48.7 
  
  
level number fixed exterior orientation [m] 
of points oX oY oZ 
L3 5474 98.4 83.0 258.9 
L2 11658 35.6 30.2 93.1 
Li 10548 22.0 18.6 $72 
LO 4757 14.3 12.1 37.4 
  
  
  
  
  
  
  
Table 1: Theoretical standard deviations of the object 
coordinates of the ray intersections using ESA 
exterior orientation. 
Table 2 shows the results after automatically removing some 
matching blunders. Compared to the values given in Table 1 the 
differences of the standard deviations are not significant. 
Table 4: Progression of the standard deviation on each pyramid 
level of orbit 18 using a fixed exterior orientation. 
  
  
  
  
  
  
  
  
level number improved ¢ and « [m] 
of points ox oY oZ 
[L3 4216 43.6 38.5 116.2 
L2 8488 25.4 22.2 67.8 
LI 6457 14.5 12.8 39.1 
LO 3776 6.6 5.9 18.0 
  
  
  
  
  
  
  
  
  
  
orbit | altitude [km] oX [m] oY [m] oZ [m] 
18 275 —347 12.1 10.7 33.4 
22 311—941 13.0 17.2 41.6 
68 269 — 505 31.2 29.2 50.6 
  
  
  
  
  
  
Table 2: Theoretical standard deviations of the object 
coordinates of the ray intersections after removing 
some matching blunders. 
The obtained values are compared to the results calculated by a 
bundle adjustment improving « and « (Table 3). This means a 
constant bias is estimated for both angles along the entire orbit. 
Biases for ¢ and x were introduced, because only these two 
parameters can be improved using tie points. Biases for the 
other four orientation parameters X0, YO, Z0 and c can only be 
determined based on ground control information. Here some 
points have also been eliminated as blunders. As can be seen 
the bundle adjustment yields higher quality tie points and 
higher achievable accuracy of the ray intersections. 
Table 5: Progression of the standard deviation on each pyramid 
level of orbit 18 after improving ¢ and x. 
Finally, the number of 5-fold points and the standard deviations 
after adjusting ¢ and x using different LSM modes are 
presented in Table 6 considering orbit 22 as example. In the 
first line the result without LSM is shown. More than 5.000 5- 
fold points have been derived via FBM. In LSM mode A all six 
affine parameters of the least squares adjustment have been 
used. 
  
  
  
  
  
  
3 number 
LSM of 5-fold oX [m] oY [m] oZ [m] 
mode 
points 
no 5533 14.3 11.8 26.4 
A 96 7.9 133 19.6 
B 1648 0.1 7.6 21.6 
C 1648 9.1 7.6 "4 21768 
  
  
  
  
  
  
  
  
  
  
  
  
orbit | altitude [km] oX [m] cY [m] oZ [m] 
18 275 —347 6.6 6.0 18.1 
22 311 —941 8.6 9.1 21.9 
68 269 — 505 11.0 10.4 17.9 
  
  
  
  
Table 3: Theoretical standard deviations of the object 
coordinates of the ray intersections after improving 
© and K. 
The standard deviations of the object points are in a range of 
about 6 to 11 m in X and Y, depending on different imaging 
altitudes. Z accuracies of all orbits are about 18 to 22 m. The 
standard deviations of the ray intersections are improved by a 
factor of 2 to 3. Presuming a pixel size of about 25 m on the 
surface, a final accuracy of about 0.4 pixel in X and Y and 0.8 
pixel in Z is achieved. 
In Table 4 the changes of the standard deviation on each 
pyramid level of orbit 18 are shown. Here the standard 
deviations have been calculated using the fixed exterior 
  
Table 6: Number of 5-fold points and accuracies using different 
LSM modes in orbit 22. 
It can be seen that the standard deviations of the ray 
intersections have been improved by applying LSM. However, 
the number of 5-fold points decreased to 96. By accounting 
only for the two shift parameters in the adjustment (LSM mode 
B) 1648 5-fold points have been obtained and the standard 
deviations lie in a similar range as for mode A. This seems to 
be a sufficient number for the bundle block adjustment. 
It is also possible to use a combination of the LSM modes A 
and B (LSM mode C), where the result of the two shift 
parameters are used as approximate values for the adjustment 
applying all six parameters. Admittedly this method yields no 
advantage in the investigated case. However, it has to be stated 
that this is no recommendation for using only the two shift 
parameters in every case. Further investigations will be carried 
out evaluating these LSM modes with different imagery. 
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