## 3 Method for Improving the Pointing Error
### Installation Error Model  
During the installation of the GPS/INS unit, inevitable installation errors are incurred between the measuring axis of the GPS/INS unit and the ATP pointing axis. If there is an error between the installation of the GPS/INS unit and the ATP, the attitude compensation accuracy will be affected and the pointing accuracy of the ATP will decrease. Therefore, after the installation of the GPS/INS unit and ATP, the rotation relationship between the platform coordinate system represented by the GPS/INS unit \(\text{O}-\text{X}_{\text{p}}\text{Y}_{\text{p}}\text{Z}_{\text{p}}\) and the shipborne ATP deck coordinate system \(\text{O}-\text{X}_{\text{c}}\text{Y}_{\text{c}}\text{Z}_{\text{c}}\) needs to be calibrated (Figure 4). When measuring the equipment attitude, it is necessary to convert the inertial attitude to the coordinate system of the equipment. The Equations (8) can be obtained from Equations (3) and (4), and [PERSON]'s theorem:  
\[\left[ \begin{array}{c}\text{X}_{\text{c}}\\ \text{Y}_{\text{c}}\\ \text{Z}_{\text{c}}\end{array} \right]=\Psi t*\xi t*\left[ \begin{array}{c} \text{x}\\ \text{y}\\ \text{z}\end{array} \right] \tag{8}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Attitudeangle** & **Accuracy** \\ \hline Yaw & \(\leq\)0.18 mrad (RMS) \\ Roll and pitch & \(\leq\)0.09 mrad (RMS) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: GPS/INS unit attitude measurement accuracy. Figure 4: Error relation between the shipborne ATP and the GPS/INS unit. We can get from Equations (3) and (4), as shown in Equation (9). \[\left[ \begin{array}{c}L\cos\mathrm{E_{c}}\!\cos\mathrm{A_{c}}\\ L\cos\mathrm{E_{c}}\!\sin\mathrm{A_{c}}\\ L\sin\mathrm{E_{c}}\end{array} \right]=\Psi t*\xi t*\left[ \begin{array}{c}L \cos\mathrm{EcosA}\\ L\cos\mathrm{EsinA}\\ L\sin\mathrm{E}\end{array} \right] \tag{9}\]  
where \(\left(\mathrm{A_{c}},\mathrm{E_{c}}\right)\) represents the target polar coordinate in the deck coordinate system, (A, E) represents the target coordinate value in the Northeast celestial coordinate system, \(\xi t\) represents the attitude rotation matrix, and \(\Psi t\) is the installation error matrix for the shipborne ATP and the GPS/INS unit. \(\Psi t\) is the parameter to be calibrated, \(\Lambda_{c}\) and \(\Lambda\) are coefficient matrices determined by experimental data, and the linear model of installation error can be expressed as Equation (10):  
\[\Lambda_{c}=\Psi t*\xi t*\Lambda+\Delta \tag{10}\]  
where, \(\Lambda_{c}=\left[ \begin{array}{c}L\!\cos\mathrm{E_{c}}\!\cos\mathrm{A_{c}} \\ L\!\cos\mathrm{E_{c}}\!\sin\mathrm{A_{c}}\\ L\!\sin\mathrm{E_{c}}\end{array} \right]\), \(\Lambda=\left[ \begin{array}{c}L\!\cos\mathrm{EcosA}\\ L\!\cos\mathrm{EsinA}\\ L\!\sin\mathrm{E}\end{array} \right]\), \(\Delta=[\alpha,\beta,\theta]^{T}\). The method of \"star tracker\" is used to evaluate the absolute pointing error of telescope, which is the main method to determine the absolute pointing error of ATP [27]. Because of the high precision of the known positions of stars in the sky, the identification of star signals provides a powerful tool for checking the absolute ATP alignment. In practical application, a star is considered a measurable point in the sky, and the least square fitting technology provides a solution for the absolute pointing error assessment [28]. In fact, we know the theoretical coordinates of the stars \(\left(\mathrm{A_{i}},\mathrm{E_{i}}\right)\) in the Northeast celestial coordinate system. When measuring the star using the shipborne ATP, the measured value of the stars \(\left(\mathrm{A_{c_{i}}},\mathrm{E_{c_{i}}}\right)\) can be obtained from the deck coordinate system. Several stars in the all-sky region were measured, and the error matrix, \(\hat{\Psi}t\) was obtained by fitting with the least square method. To sum up, the undetermined parameter \(\hat{\Psi}t\) of the installation error model is calibrated by the least square method, and the residual error \(\Delta\) is calculated by substituting into Equation (10).