Considering the scene orientation angle A between 
the orbital direction and Y axis of the local 
coordinate system, the displacement at a instant 
corresponding scene center can be expressed as: 
acosB W.t 
dar 0 cos À (4) 
x 
AY 1-e? snp 
sin A = cos I (4 1) 
cos $ 
Where, I represents the angle of SPOT orbit 
incidence, and ¢ expresses the geocentric latitude of 
point Py. Generally, B and ¢ for an image point can 
be calculated by interpolation according to the 
latitude and geocentric latitude of scene center and 
four corner points. 
Earth rotation also causes the variance of scale 
factor in y-direction of scene (i. e. SPOT orbit 
direction). The variance is no effect on time serial 
of scene. Therefore it will not be discussed in this 
paper. 
3. THE POSSIBILITY OF SPOT SCENES 
ADJUSTMENT WITHOUT GROUND 
CONTROL POINTS 
As described above, the number of GCP needed to 
make the adjustment can be reduced obviously due 
to the application of ephemeris data. If the 
geographic coordinates of scene corner and center as 
well as attitude data are employed, it is possible to 
take the adjustment without GCP fora particular 
level of accuracy. 
In SPOT CCT, pitch (w), roll (¢), and yaw (x) 
drift rates are supplied at a 0.125 second interval. 
The value of the drift rate at instant t; can be 
calculated by linear interpolation. Then, by 
integrating these rates from the instant to for scene 
center to t; , the pointing variance of sensor at 
instant t; , with respect to scene center instant t 0 
can be obtained. 
n 
t 
af vdt= X v (Py;-Py, ) t, (5) 
to i1 
1= 
where n represents the number of points included 
from instant t; to t, 
70 
The averaged velocities ¢,, «,, x, of variances for 
9, 0, x can be calculated in formula (5) according to 
72 or 73 attitude data respectively. In this case, the 
averaged velocity in formula (2--1) become known 
constants.Therefore , the unknown parameters in 
formula (2) are reduced to 20. 
Excluding attitude data, the geographic coordinates 
of corner and center of scene can also be employed 
as pseudo control conditions. The image coordinates 
corresponding to the pseudo control points are 
constants and can be obtained from SPOT CCT. 
Using the data above, the adjustment without GCP 
for SPOT scenes can be realized. 
4. TEST AND ANALYSIS 
A group of programs for simultaneous bundle 
adjustment for SPOT scenes using orbital data 
and a few ground control points has been 
developed. The flow chart of the programs is shown 
in figure 2. 
The results for tests reported here are from three 
different stereo scenes: STF (France), STC (China) 
and STU (USA). The results are shown in Table 1. 
In test STF, the orbital data are not included. The 
results demonstrate the practical effect of earth 
rotation. It is obvious from Table 1 that the fewre 
the number of GCP, the more important the 
correction for earth rotation. The test indicates that 
the error due to earth rotation can not be removed 
completely if the coordinates of image points are not 
  
  
     
Ephemeris 
data 
Interpolation of Coordinates Coordinates of 
sensor position translation center & corner 
/ 
Constraints mage coord. Pseudo control 
| equations correction equations 
    
    
   
  
   
     
   
  
  
  
  
  
   
  
  
  
  
  
   
Formation & 
adjustment of 
block net 
  
     
  
  
/ 
End 
  
  
  
  
Figure 2 Flow chart of programs 
  
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