The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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The real on-orbit camera parameters are set as follow, 
f 0 =3660.97(p), ; o =35(p), ; o =35(p), k \ = 3e-8(p' 2 ) k 2 = 
le-13(p‘ 4 ),(Note: p denotes pixel, and the below is the same). 
The camera parameters before calibration are given as below, 
/o=3655.97(p),x 0 =0(p),yo=0(p), *, = 0(p 2 ), k 2 =0(p A ). 
4.1 The calibration experiment based on the single image 
and multi-images 
After the real camera parameters and the attitude angles are 
given, the star image point coordinates can be simulated, then 
each image point is added with the position error 0.1 pixel. Ten 
continuous images in the one calibration period are selected. 
First, the calibration is done using each star image data 
independently, then the process is repeated using all ten images, 
the calibration results are shown in table 1. (Note: the 
calibration accuracy is denoted by absolute difference value of 
the calibrated parameter values and the real parameter values). 
Camera 
Parameters 
accuracy 
Af 
(P) 
Ax 0 
(P) 
Ay 0 
(P) 
Ak, 
(P 2 ) 
(Iff 9 ) 
Ak 2 
(F 4 ) 
(Iff 14 ) 
Singl 
e 
imag 
e 
1 
2.01 
8.75 
11.25 
23.51 
20.45 
2 
9.77 
4.50 
7.63 
77.57 
49.30 
3 
18.15 
61.80 
37.10 
130.6 
0 
70.93 
4 
16.84 
300.3 
9 
207.4 
9 
21.01 
19.99 
5 
0.7 
1.70 
1.04 
6.23 
4.92 
6 
1.26 
11.90 
6.99 
19.11 
8.89 
7 
0.16 
6.44 
0.72 
15.91 
25.67 
8 
2.55 
0.37 
5.13 
13.78 
8.85 
9 
2.00 
42.87 
24.45 
9.18 
13.07 
10 
0.64 
4.46 
17.45 
6.00 
1.93 
ten images 
0.57 
1.97 
1.37 
3.89 
3.67 
Table 1. Calibration result based on single image and ten 
images separately 
It can be seen from table 1, of all the calibration results based 
on each single image, only these using the fifth, seventh, eighth 
and tenth image are relatively good, although the accuracy isn’t 
high. The calibration results based on the other images are 
worse. As seen from figure 3, the good calibration results are 
based on the images which have good distribution. But for most 
other image, the natural distribution of it is difficult to satisfy 
the calibration requirement, so the calibration accuracy is low 
From table 1, the calibration result is based on all ten images is 
better than based on each single image. The reason is that there 
are only three unknowns for each star image, but this image can 
provide three control points at least to calibrate the camera 
parameters, when the star images which have good distribution 
is added for calibration, the calibration accuracy become better. 
4.2 The relationship between the calibration accuracy and 
the number of images 
Suppose that the camera parameters before and after calibration 
are same with experiment above, when the random position 
error 0.1 pixel is added in the image coordinates, the calibration 
experiments are done with 1-10 images separately, the 
relationships between the number of the images and the 
principle distance, the principle points and the distortion 
coefficients are shown in figure 5,6,7,8. 
Figure 5. The relationship between the principle distance and 
the number of images 
Figure 6. The relationship between the principle point and the 
number of images 
Akl 
Figure 7. The relationship between the distortion 
coefficient k] and the number of images