## 4 Experiment and Results  
We developed a shipborne ATP system (Figure 6) mainly to verify the ability for acquisition and pointing, hence, a fast-steering mirror was not used at the fine pointing stage. The primary mirror in the ATP system is a reflecting Cassegrain telescope with an aperture of 75 mm and a focal length of 200 mm. The coarse-control loop included a two-axis gimbal telescope (azimuth rotation range of about \(-360^{\circ}\) to \(+360^{\circ}\), elevation rotation range of about \(-5^{\circ}\) to \(+90^{\circ}\)) and a CCD camera (FOV of \(0.97^{\circ}\times 0.91^{\circ}\), frame rate of 50 Hz).  
Figure 5: Installation and systematic error model calculation and application process. (**a**) Installation and system error model calculation flow chart. (**b**) Flow chart of actual use.  
Figure 6: The shipborne ATP system. The shipborne ATP system shows the uplink beacon, coarse camera, and the attitude pre-compensation unit.  
We set up the ATP system terminal on an experimental ship at Dalian city. After the installation of the ATP system, the experimental ship sailed to an experimental site (38\({}^{\circ}\)48.027\({}^{\prime}\) N, 121\({}^{\circ}\)50.037\({}^{\prime}\) E) in the sea. We calibrated the ATP system's pointing ability by tracking and measuring a batch of stars one hour before the experiment. The residual error after installation error correction is shown in Figure 7 while the residual error after systematic error correction is shown in Figure 8. After obtaining the ATP system error model, a batch of stars were tracked and measured to verify the accuracy of the system error model. We used the shipborne ATP to track 15 stars with open-loop and obtained the pointing accuracy. The absolute pointing error obtained for the shipborne ATP azimuth was117.8\(\upmu\)rad whereas the elevation was 128.1\(\upmu\)rad (Figure 9). The total pointing error of ATP is given by \(\delta_{\text{pointing error}}\) as shown Equation (13).  
\[\delta_{\text{pointing error}}=\sqrt{\delta_{\text{azimuth}}{}^{2}+\delta_{ \text{elevation}}{}^{2}}=0.174\text{ mrad} \tag{13}\]  
Figure 7: Residual error after installation error calibration. The azimuth residual error is 654.2\(\upmu\)rad while the elevation residual error is 195.6\(\upmu\)rad.  
Figure 10 shows the performance of the shipborne ATP with respect to the acquisition and tracking of a satellite. The azimuth and elevation tracking errors were both less than 20\(\upmu\)rad (RMS). The azimuth and elevation tracking errors were both less than 20\(\upmu\)rad (RMS).  
initial acquisition error was 310\(\upmu\)rad whereas the elevation initial acquisition error was160\(\upmu\)rad. This error includes the orbital error of the satellite.  
Figure 10: The shipborne ATP acquired and tracked the performance of a satellite. (**a**) The tracking error for the entire process and the initial error just appear in the field of view. The azimuth initial acquisition error was 310\(\upmu\)rad whereas the elevation initial acquisition error was 160\(\upmu\)rad. When the spot was in the tracking field, the azimuth tracking error was about 19.5\(\upmu\)rad (RMS) while the elevation tracking error was about 14.6\(\upmu\)rad (RMS). The tracking error in the stabilized time lasted from 10:15:58 to 10:21:28, about 330 seconds. (**b**) Ship attitude measurement. The yaw, pitch, and roll curves of the ship measured by the GPS/INS unit.