## 3 Ultra-Long-Range Scanning and Acquisition Technology
### Star Calibration for Optical Axis  
By obtaining the geodetic coordinates (latitude, longitude, altitude) of the two terminals from GPS, coordinate transformation can be used to calculate the azimuth and elevation angles required for the terminal to point at the target. To minimize errors, star observations are employed, using the star's elevation and azimuth angles as references to correct the azimuth and elevation angles of the PAT terminal. This ensures consistent calculations across the terminals and reduces errors between them. Dual GPS antennas are used to measure the angle between the PAT terminal's initial position and true north, providing the initial azimuth for star observation [20; 21]. The theoretical azimuth angle calculation formula is as follows:  
\[\theta_{FW}=-\theta_{GNSS}\pm 90^{\circ}+\theta_{FW-STK}+\sigma_{FW}\quad, \quad\theta\in(-180^{\circ},180^{\circ}) \tag{6}\]  
where \(\theta_{GNSS}\) is the azimuth angle obtained from GNSS, \(\pm 90^{\circ}\) is determined by the relationship between the baseline and the PAT terminal's zero position, \(\theta_{FW-STK}\) is the azimuth angle provided by Satellite Tool Kit (STK11.0) software, and \(\sigma_{FW}\) is the azimuth angle correction value. The theoretical elevation angle calculation formula is as follows:  
\[\theta_{FY}=\theta_{FY-STK}+\sigma_{FY}\quad,\quad\theta\in(-90^{\circ},90^{ \circ}) \tag{7}\]  
where \(\theta_{FY-STK}\) is the elevation angle provided by STK, and \(\sigma_{FY}\) is the azimuth angle correction value. Since we can obtain the azimuth and elevation angles of the selected star relative to the PAT terminal's body coordinate system from the ephemeris, we can use these angles to correct the azimuth and elevation angles when the PAT terminal observes the star. Before calibration begins, the PAT terminal must be installed completely horizontally on the ground, and the absolute azimuth of the PAT terminal is measured using dual-station GPS. Using the STK software, we obtain the azimuth and elevation angles of the star to be  
Figure 3: Schematic of dual-station GPS measurement installation. observed at a specific time and calculate the azimuth and elevation angles the PAT terminal must control to point at the star. These values are then input to the PAT terminal. After the PAT terminal rotates according to the input azimuth and elevation angles, the presence of the target star in the CCD field of view is checked. When the star image appears in the CCD field of view, as shown in Figure 4, if the star is not visible, the PAT terminal's elevation angle is quickly adjusted in a small range until the target star appears in the field of view. Once the star appears in the field of view, the PAT terminal is fine-tuned so that the star's trajectory passes through the center of the field of view. After the star passes through the center of the field of view, the PAT terminal telemetry data are checked, and the time at which the star passes the center of the field of view, along with the PAT terminal's azimuth and elevation angles, are recorded as the \"actual elevation angle\" and \"actual azimuth angle\". The corresponding theoretical elevation angle and azimuth angle are then calculated from the STK software for the star at that moment, which are referred to as the \"theoretical elevation angle\" and \"theoretical azimuth angle\". By comparing the theoretical and actual elevation and azimuth angles, the difference is obtained, providing the correction value for the PAT terminal's optical axis. To minimize the error, this calibration process can be iterated multiple times. Once the ideal correction value is obtained, the azimuth and elevation angles required for the two optical communication terminals to point at each other can be easily calculated.