## 3 Method for Improving the Pointing Error
### Installation and Systematic Error Model Calculation and Application Process  
The installation and systematic error model can be obtained by the shipborne ATP's software automatically as shown in Figure 5a. ATP tracks and measures about 20 stars (magnitude less than 6, etc.) uniformly throughout the sky. Then the star's theoretical position \((\mathrm{A}_{\mathrm{i}},\mathrm{E}_{\mathrm{i}})\), measurement position \((\mathrm{A}_{\mathrm{c_{i}}},\mathrm{E}_{\mathrm{c_{i}}})\), and ship attitude \((\mathrm{H}_{\mathrm{i}},\mathrm{P}_{\mathrm{i}},\mathrm{R}_{\mathrm{i}})\) can be recorded. Once the measurements are available, the telescope will automatically track and measure the next star. The installation error matrix and systematic error model are solved by the least square method after all the stars measurement data are obtained. The whole process takes less than 10 min.  
In the acquisition mode, the ideal point angle (A, E) in the Northeast celestial coordinate system is calculated according to the relationship between the target guidance position and the position of the ship. According to the measured attitude (H, P, R) and the installation error matrix \(\Psi t\), the guidance value \((\mathrm{A}_{\mathrm{c}},\mathrm{E}_{\mathrm{c}})\) in the deck coordinate system can be calculated. Then, according to the pointing error correction model, the pointing error \((\Delta\mathrm{A}_{\mathrm{c}},\Delta\mathrm{E}_{\mathrm{c}})\) corresponding to the \((\mathrm{A}_{\mathrm{c}},\mathrm{E}_{\mathrm{c}})\) pointing angle is solved. Finally, the pointing error \((\Delta\mathrm{A}_{\mathrm{c}},\Delta\mathrm{E}_{\mathrm{c}})\) is used to correct the actual pointing angle \((\mathrm{A}_{\mathrm{c}},\mathrm{E}_{\mathrm{c}})\), and the correct pointing angle \((\mathrm{\hat{A}}_{\mathrm{c}},\mathrm{\hat{E}}_{\mathrm{c}})\) is obtained as shown in Figure 5b.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Term** & **Description** & **Azimuth Function (Y)** & **Elevation Function (\(\Gamma\))** \\ \hline
1. & Azimuth encoder offset & 1 & - \\
2. & Elevation encoder offset & - & 1 \\
3. & Azimuth axis tilt about & \(-\cos\mathrm{A}_{\mathrm{c}}\mathrm{tan}\,\mathrm{E}_{\mathrm{c}}\) & \(\sin\mathrm{A}_{\mathrm{c}}\) \\  & fore-and-aft line & \(-\sin\mathrm{A}_{\mathrm{c}}\mathrm{tan}\,\mathrm{E}_{\mathrm{c}}\) & \(-\cos\mathrm{A}_{\mathrm{c}}\) \\
4. & Azimuth axis tilt about axis \(\mathrm{Y}_{\mathrm{c}}\) & \(-\sin\mathrm{A}_{\mathrm{c}}\mathrm{tan}\,\mathrm{E}_{\mathrm{c}}\) & \(-\cos\mathrm{A}_{\mathrm{c}}\) \\
5. & optical axis misalign & \(\sec\mathrm{E}_{\mathrm{c}}\) & - \\
6. & Non-orthogonality of Azimuth & \(-\tan\mathrm{E}_{\mathrm{c}}\) & - \\  & and Elevation axes & \(-\tan\mathrm{E}_{\mathrm{c}}\) & - \\
7. & Azimuth bearing ellipticity (sin) & \(\sin\mathrm{A}_{\mathrm{c}}\) & - \\
8. & Azimuth bearing ellipticity (cos) & \(\cos\mathrm{A}_{\mathrm{c}}\) & - \\
9. & Azimuth bearing ellipticity (sin) & - & \(\sin\mathrm{E}_{\mathrm{c}}\) \\
10. & Azimuth bearing ellipticity (cos) & - & \(\cos\mathrm{E}_{\mathrm{c}}\) \\
11. & Telescope tube flexure & - & \(\cot\mathrm{E}_{\mathrm{c}}\) \\
12. & Azimuth encoder scale error & \(\mathrm{A}_{\mathrm{c}}/2\pi\) & - \\
13. & Elevation encoder scale error & - & \(\mathrm{E}_{\mathrm{c}}/2\pi\) \\
14. & Bi-periodic in azimuth & \(\cos 2\mathrm{A}_{\mathrm{c}}\) & - \\
15. & Elevation encoder stiction & - & \(\sin\mathrm{A}_{\mathrm{c}}\) \\
16. & Elevation bearing stiction & - & \(\mathrm{E}_{\mathrm{c}}\mathrm{sin}\,\mathrm{A}_{\mathrm{c}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The ATP mount model.