An along-track stereopair can be orientated using as few as 3 
control points per image, providing 12 observation equations, 
for the 11 parameter solution. The number of control points may 
be decreased if a poorer orientation is adopted, for example 
when 2 control points per image are used, then a 7 parameter 
orientation is possible with some redundancy. 
It has been shown (O'Neill et al, 1989) that better results may 
be obtained if on-board recorded information is used. The 
algorithm automatically takes an a priori precision of the 
measurements, the control used in the orientation plus 
information recorded during flight. Initial information of the 
start values is used to form a weighting matrix. Currently, the 
algorithm implemented uses information in an auxiliary data file 
with additional information being provided by the user. 
4. SIMULATED DATA 
Tests in order to study the precision of the orbital model 
described above were performed. The data used was simulated 
since no satellite along-track stereo data is presently available. 
Two sets of SPOT data covering a region in south-east France 
(about 200 per 600 km), available at UCL(P&S) (Veillet, 
1991), were used to calculate the orbital parameters of a vertical 
theoretical SPOT-like orbit. 
The simulated image coordinates of 106 ground points were 
computed using equation 10 and their known geocentric 
coordinates. The iterative process was run for two different 
along-track viewing angles, terminating when a correction 
smaller than 0.001mm was encountered for x=0 (this correlates 
to an error smaller than 0.1 line/sample). 
Xa - Xs 
1 
Y |=--RnRaRo| Ya- Ys (10) 
4j: Z a - Zs 
À first set of images simulate backward and forward angles of 
26°, emulating a SPOT-like along-track stereopair with a base to 
height ratio of approximately 1. À second simulation calculated 
both ASTER-like, OMI and OPS sensor data. All simulations 
used Westin’s variogram (Westin, 1991), which models the 
variation of the attitude parameters with time. À pseudo-error 
with standard deviation 0.5 line/sample was added to the 
simulated data, as an average error of half a pixel of 
identification ia the points on the image may be assumed. 
In the OEEPE tests (Dowman et al, 1991) it was concluded that 
the results underwent only small variations when more than six 
control points were used in the orientation. Hence, six points 
were chosen from the simulated data for ground control, the 
other one huncred points being used for checking purposes. 
5. RESULTS OF TESTS 
The scenes were orientated using the control configuration 
shown in figure 5, with the control distribution of the terrain 
318 
being chosen such that it would cover all types of relief possible 
and would be well distributed for better orientation. 
  
  
  
  
  
  
  
  
  
  
  
  
. e e e e . 
e e e 
e 9 e e 
e 9 
© e €. e. e 
6 cpts 5 cpts 4 cpts 3 cpts 2 cpts 
Figure 5 - Control configuration used in the tests 
The same configuration was used to orientate the different sets 
of simulated data. The root mean square(rms) of the errors 
obtained with the check data are presented in tables 2, 3, 4 and 
5. The 2 control points models were run using only 7 
orientation parameters, plus At . The only attitude parameter 
variation with time considered in the computation was that of 
pitch due to its larger effect on height, and the bias in roll being 
fixed using the attitude file information. The models respective 
precisions were evaluated by comparing the UTM (Universal 
Transverse Mercator) coordinates calculated after orientation, to 
the known simulated coordinates of the 100 check points not 
used in the model processing. 
The precisions obtained using the SPOT-like along-track 
stereopair (10 m pixel resolution) are given in table 2. 
Analogous results for the ASTER (15 m pixel resolution), OMI 
(5 m pixel resolution) and OPS (18.3x24.1 m pixel resolution) 
are given in tables 3, 4 and 5 respectively. 
  
  
  
  
  
  
  
Number of rms of errors found in UTM (m) 
control points E N H 3D 
6 S.2 5.3 5.9 9.5 
S 7.0 6.5 7.6 12.2 
4 7.0 6.5 7.6 12.2 
3 8.7 5.1 9.4 13.8 
2 10.1 6.7 8.8 15.0 
  
  
  
  
  
  
  
Table 2 - Precision obtained for a SPOT-like simulated orbit 
with along-track stereo viewing (10m pixel resolution). 
  
Number of rms of errors found in UTM (m) 
control points E N H 3D 
7.9 8.6 19.6 | 22.8 
9.1 10.4 17.8 22.5 
9.1 10.4 17.8 22.5 
73 14.2 194 | 23.4 
6.9 6.7 24.5 29.1 
  
  
  
  
  
  
ViWISR iW 
  
  
  
  
  
  
  
Table 3 - Precision obtained using ASTER simulated data 
(15m pixel resolution).