## 3 Method for Improving the Pointing Error
### Pre-compensation for Ship Platform Attitude
\begin{array}{cccc}\cos \,\rm P&0&\sin\,\rm P\\ 0&1&0\\ -\sin\,\rm P&0&\cos\,\rm P\end{array} \right]\left[ \begin{array}{cccc}\cos \,\rm H&\sin\,\rm H&0\\ -\sin\,\rm H&\cos\,\rm H&0\\ 0&0&1\end{array} \right] \tag{3}\]  
Figure 2: Schematic diagram of coordinate system and attitude angle. (**a**) The Northeast celestial coordinate system \(\rm O\)-\(\rm XYZ\). (**b**) The deck coordinate system \(\rm O-X_{c}Y_{c}Z_{c}\). (**c**) Definition of attitude angle. The conversion expression is shown in Equation (4) below:  
\[\left[ \begin{array}{c}\mathrm{x_{c}}\\ \mathrm{y_{c}}\\ \mathrm{z_{c}}\end{array} \right] =\xi t\left[ \begin{array}{c}\mathrm{x}\\ \mathrm{y}\\ \mathrm{z}\end{array} \right] \tag{4}\] \[=\left[ \begin{array}{ll}\cos\mathrm{HcosP}&\sin\mathrm{HcosP}& \sin\mathrm{P}\\ -\sin\mathrm{HcosR}-\cos\mathrm{HsinPsinR}&\cos\mathrm{HcosR}-\sin\mathrm{HsinPsinR }&\cos\mathrm{PsinR}\\ -\cos\mathrm{HsinPcosR}+\sin\mathrm{HsinR}&-\sin\mathrm{HsinPcosR}-\cos \mathrm{HsinR}&\cos\mathrm{PcosR}\end{array} \right]\left[ \begin{array}{c} \mathrm{x}\\ \mathrm{y}\\ \mathrm{z}\end{array} \right]\]  
It can be obtained the Equation (5) from Equations (1) and (2):  
\[\left\{ \begin{array}{ll}\mathrm{A_{c}}&=\mathrm{arctg}(\frac{\mathrm{y_{c}} }{\mathrm{x_{c}}})\\ \mathrm{E_{c}}&=\mathrm{arcsin}(\frac{\mathrm{y_{c}}}{\mathrm{L}})\end{array} \right. \tag{5}\]  
Thus, the target guidance value under the deck coordinate system can be obtained, as shown in Equation (6):  
\[\left\{ \begin{array}{ll}\mathrm{A_{c}}&=\mathrm{arctg}[\frac{\cos\mathrm{E }\ [\cos\mathrm{R}\ \sin(\mathrm{A-H})-\sin\mathrm{P}\ \sin\mathrm{R}\ \cos(\mathrm{A-H})]+\sin\mathrm{E}\ \cos\mathrm{P}\ \sin\mathrm{R}}{\cos\mathrm{E}\ \cos\mathrm{P}\ \cos(\mathrm{A-H})+\sin\mathrm{E}\ \sin\mathrm{P}}]\\ \mathrm{E_{c}}&=\mathrm{arcsin}[\sin\mathrm{E}\ \cos\mathrm{P}\ \cos\mathrm{R}-\cos \mathrm{E}[\sin\mathrm{R}\ \sin(\mathrm{A-H})+\sin\mathrm{P}\ \cos\mathrm{R}\ \cos(\mathrm{A-H})]]\end{array} \right. \tag{6}\]  
It can be seen from Equation (6) that the measurement accuracy for attitude (H, P, R) is one of the key factors affecting the accuracy of shipborne ATP pointing. The attitude error of the shipborne ATP is the main source of error that affects the orientation of the line-of-sight. We used an attitude pre-compensation unit (Figure 3), which used a combined inertial navigation equipment composed of a gyroscope, accelerometer, and GPS (GPS/INS) to measure the attitude of the ship. We made pre-compensation for the attitude by 200 Hz, compensating for the wobble of the ATP line-of-sight axis caused by the swaying of the ship. The attitude error of the shipborne ATP is the main source of error that affects the orientation of the line-of-sight. The attitude of the ship is measured by the GPS/INS unit, which is converted into a compensation amount for the ATP line-of-sight axis for real-time attitude compensation using Equation (6). The accuracy of the GPS/INS unit measurement is shown in Table 1. The angle measurement error for the GPS/INS unit roll and pitch direction root-mean-square (RMS) was \(\delta_{\mathrm{Pitch}}=\delta_{\mathrm{Roll}}=0.09\mathrm{mrad}\) (root-mean-square.) whereas the yaw direction angle measurement error was \(\delta_{\mathrm{Yaw}}=0.18\mathrm{mrad}\) (RMS). Figure 3: Attitude pre-compensation unit. From Equation (6), the target guidance error caused by the GPS/INS unit can be obtained as shown in Equation (7), \(\delta_{\text{azimuth}}=0.18\text{mrad}\) (RMS) and \(\delta_{\text{elevation}}=0.09\text{mrad}\) (RMS). \[\delta_{\text{guidance}}=\sqrt{\delta_{\text{azimuth}}^{2}+\delta_{\text{elevation}}^{2}}=0.202\text{mrad} \tag{7}\]  
To improve the precision of the attitude compensation, the ship's attitude at the present moment as measured by the GPS/INS unit is used to predict the ship's attitude at a future time, while the guidance value of the target is pre-compensated. We used attitude velocity filtering and extrapolation to compensate the attitude lag.