71 
ON-ORBIT STELLAR CAMERA CALIBRATION BASED ON SPACE RESECTION 
WITH MULTI-IMAGES 
Xie Junfeng 3 , Jiang Wanshou 3 *, Gong Jianya 3 *, Wang xiao 3 
3 State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, 
Luoyu Road 129, Wuhan, China, 430079 -junfengxie@gmail.com (jws,jgong)@lmars.whu.edu.cn 
wclearwaters@gmail.com 
KEY WORDS: on-orbit calibration, stellar camera, space resection, multi star images, satellite attitude accuracy 
ABSTRACT: 
Due to the intense vibration and/or the change of space environmental factors such as temperature, pressure, etc., the stellar camera 
parameters might change during satellites launching or while orbiting the earth, which causes the decline of satellite attitude 
accuracy. So the on-orbit calibration is essential for the stellar camera. In this paper, the selection of star image for on-orbit 
calibration is discussed. From experiment, it can be concluded that for the on-orbit calibration based on space resection, the 
distribution of star image points has strong effect on the calibration accuracy, and a good selection of images can significantly 
improve the calibration accuracy. 
1. INTRODUCTION 
Satellite attitude determination is not only the basis of satellite 
attitude control, but also one of the effective means to improve 
the direct location accuracy of remote sensed imagery (spot 
image, 2005). At present, attitude determined by star sensor is 
one of main satellite attitude determination methods (Levine et 
al., 1991; Jorgensen and Pickles, 1998; Eisenma and Liebe, 
1997 ). 
There are many factors affecting the accuracy of satellite 
attitude determined by star sensor, and the calibration accuracy 
of the stellar camera parameters is an important factor (Xie, 
2007). Although the stellar cameras parameters have been 
calibrated on the ground before the satellite launches, the 
camera parameters might change when the satellite had intense 
vibration in the process of launching and/or the space 
environmental elements such as temperature, pressure, etc. have 
changes. All of them will cause the decline of the stellar camera 
parameters accuracy directly. Therefore, the on-orbit calibration 
for stellar camera is very essential to assure the attitude 
accuracy. 
So far, there are a few on-orbit calibration methods for the 
stellar camera. US Texas T&M University Ju and Samaan 
proposed a calibration method to calibrate the interior 
orientation elements of the stellar camera, which uses the 
equation of the sine or cosine of two angle distances. One angle 
distance is denoted by two star image points in one image, and 
another is described by the right ascension and the declination 
of two corresponding guide stars (Ju, 2001; Samaan, 2003). 
Chen had researched a on- orbit calibration method for star 
sensor with gyro (Chen and Geng, 2006). Wang puts forward a 
stellar calibration method for the ground camera on the ground. 
This method directly considers the stars as the control points, 
and calibrates the camera parameters based on space resection 
(wang, 1979). This approach is adopted for on-orbit 
measurement of the stellar camera parameters in this paper. 
In this approach, because the Field Of View (FOV) of the 
stellar camera is narrow, the number and distribution of stars in 
one single image acquired at each moment is not necessarily 
beneficial for the stellar camera calibration. When the satellite 
orbits the earth, a large number of stellar images can be 
obtained by the stellar camera in a short time, and the 
environment factors has little effect on the stellar cameras 
within this time, so the camera parameters can be considered 
unchanged, then multi images can be accumulated to improve 
the quality of control points. At present, dozens of even 
hundreds of star images acquired within a few minutes have 
been used to calibrate the stellar camera (JU, 2001). But it 
doesn’t take into account whether the distribution of stars affect 
the calibration result, and it generally uses all identified star 
images directly, but the more number of star images doesn’t 
necessarily mean the higher calibration accuracy. Moreover, it 
may take long time for calibration. Therefore, selection of 
Image in view of the distribution is a problem needed be 
considered in this approach. 
2. ON-ORBIT CALIBRATION BASED ON THE SPACE 
RESECTION 
2.1 The principle of the on-orbit calibration 
On-orbit calibration for stellar camera uses the star image point 
coordinates as observations, and error equations of unknown 
parameters can be established based on the collinearity equation. 
The unknown parameters include the attitude angles and the 
stellar camera parameters. The camera parameters contain the 
principal point offset (jt ft y 0 ) and the focal length (/), the optical 
distortion of the CCD, mainly including the radial distortion 
and the tangential distortion, etc.. The radial distortion 
coefficients are denoted by K,, K 2 .Since the tangential 
distortion of CCD has little impact on attitude accuracy, it isn’t 
considered in this paper. 
The camera parameters before calibration are thought as initial 
values. Likewise, the attitude angles solved based on the 
collinearity equation with the initial camera parameters are