# Research into Image Point Positioning Compensation of a High-Orbit Thermal Infrared Staring Camera
## 3 Experimental Results and Analysis
### Internal and External Parameter Error Compensation Experiment  
The relative installation angle error (Table 2) is increased. The probe pointing angle of the virtual grid point in the camera coordinate system is calculated and then converted to the body coordinate system through the setting of relative installation angle to obtain the pointing angle deviation in the body coordinate system, as shown in Figure 6. \begin{table}
\begin{tabular}{c c} \hline \hline
**Installation Angle Error** & **Value** \\ \hline \(\alpha/arc\sec\) & 72 \\ \(\beta/arc\sec\) & \(-\)72 \\ \(\theta/arc\sec\) & 72 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relative installation angle error parameters. Figure 5: Pointing angle difference diagram after internal parameter compensation. (**a**) Pointing angle difference in X direction; (**b**) pointing angle difference in Y direction. Figure 6: _Cont._The internal and external parameters, respectively, calculated by the four schemes, are used to calculate the pointing angle of the compensated grid point in the body coordinates, and then the difference is found with the pointing angle calculated by the real internal and external parameters, as shown in Figures 7-10. The internal and external compensation parameters calculated from the above four schemes are used for the compensation calculation of the image point positioning of the target track. The positioning error after compensation is shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Internal Only** & **External Only** & **External before** & **Internal before** & **Before Error** \\  & & **Internal** & **External** & **Compensation** \\ \hline X direction/pixel & \(-\)27.459 & \(-\)2.268 & \(-\)1.859 & \(-\)0.608 & \(-\)28.414 \\ Y direction/pixel & \(-\)38.781 & \(-\)3.895 & \(-\)2.313 & \(-\)0.875 & \(-\)32.701 \\ Total error/pixel & 47.518 & 4.507 & 2. 967 & 1.065 & 43.321 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Positioning error after four compensation schemes. Figure 6: Parameter changes in four compensation schemes. In the figure, ‘ICO’ refers to internal compensation only, ‘ECO’ refers to external compensation only, ‘ICBEC’ refers to internal compensation before external compensation, and ‘ECBIC’ refers to external compensation before internal compensation. (**a**) xa0–xa4 parameter change; (**b**) xa5–xa9 parameter change; (**c**) ya0–ya4 parameter change; and (**d**) ya5–ya9 parameter change. Figure 7: Pointing angle difference diagram only after internal compensation scheme. (**a**) Pointing angle difference in X direction; (**b**) pointing angle difference in Y direction. Figure 8: Pointing angle difference diagram only after external compensation scheme. **(a)** Pointing angle difference in X direction; **(b)** pointing angle difference in Y direction. Figure 10: Pointing angle difference diagram of the compensation scheme of the external first and then the internal. (**a**) Pointing angle difference in X direction; **(b)** pointing angle difference in Y direction. Figure 9: Pointing angle difference diagram of the compensation scheme of the internal first and then the external. (**a**) Pointing angle difference in X direction; **(b)** pointing angle difference in Y direction. In the process of two-dimensional imaging, three-direction errors are added to the attitude parameters and orbital position parameters, and distortion errors are added to the camera parameters as the positioning results before error compensation. The positioning results before and after error compensation are compared with the theoretical values to obtain the optimal compensation scheme (as shown in Table 3). It can be seen from the experimental results that the error compensation accuracy of the four error compensation schemes, namely, the internal first and then the external, the external first and then the internal, the external only, and the internal only, decreases sequentially.