# Research into Image Point Positioning Compensation of a High-Orbit Thermal Infrared Staring Camera
## 3 Experimental Results and Analysis  
### Two-Dimensional Pointing Angle Experiment  
The orbital height of the geosynchronous orbit satellite studied in this paper is 36,000 km. Although the three-axis stability for the research object of this paper is the geosynchronous orbit satellite, the ambient temperature changes drastically [14]. The drastic temperature difference will cause the installation bracket of the camera to deform violently, and the installation angle of the camera will also change accordingly, resulting in the same effect as the attitude error. For the image point positioning error, we collected the observation data of different seasons and different times of the day in a year and established the error empirical model of the camera installation angle related to temperature and time (as shown in Figure 3).  
According to the camera's internal distortion parameters (as shown in Table 1), assuming that there is no external parameter error, the actual two-dimensional pointing angle coordinates of each grid point in the camera coordinate system are calculated, and the difference between the two-dimensional pointing angle and the initial coordinate value is calculated, as shown in Figure 4. It can be seen that after the distortion parameter is added, the difference of the two-dimensional probe pointing angle of the camera can represent the geometric distortion of the camera.  
\begin{table}
\begin{tabular}{c c c} Image principal point \(\Delta x/pixel\) & Image principal point \(\Delta y/pixel\) & Focal length \(\Delta f/mm\) \\ \(-0.0015\) & \(-0.0015\) & 1 \\ Radial distortion \(k_{1}/pixel^{-2}\) & Eccentric distortion \(p_{1}/pixel^{-1}\) & Eccentric distortion \(p_{2}/pixel^{-1}\) \\ \(5\times 10^{-11}\) & \(6\times 10^{-8}\) & \(-3\times 10^{-8}\) \\ Area array tilt \(\varphi_{x}/arc\sec\) & Area array tilt \(\varphi_{y}/arc\sec\) & Area array rotation \(\beta/arc\sec\) \\ \(-8\) & \(-8\) & \(-8\) \\ \end{tabular}
\end{table}
Table 1: Target image simulation parameters.  
According to the internal distortion parameters of the designed camera, it is assumed that there is no external parameter error; that is, there is only internal geometric distortion error. The actual two-dimensional pointing angle coordinates of each grid point in the camera coordinate system are calculated, and the difference between the actual two-dimensional pointing angle and the initial pointing angle is used to reflect the distortion inside the camera. According to the internal parameter solution method introduced in Section 2.1, the internal error compensation is performed on the distorted two-dimensional pointing angle, and the difference between the compensated two-dimensional pointing angle and the initial pointing angle is obtained (as shown in Figure 5). It can be clearly seen that the interpolation of the two-dimensional pointing angle after compensation is reduced, and the fitting accuracy can reach the millimeter level, which verifies the effectiveness of the internal error compensation scheme proposed in this paper.  
Figures 4 and 5 show the effectiveness of the two-dimensional pointing angle model proposed in this paper in solving the internal compensation parameters.  
Figure 4: Pointing angle difference diagram after camera distortion. (**a**) Pointing angle difference in X direction; (**b**) pointing angle difference in Y direction.  
Figure 3: Curve of relative installation angle and time change.