# Test Method for Single Satellite's Inter-Satellite Link Pointing and Tracking via Ground Station
###### Abstract
studied the method of calculating the pointing angles of transmission devices based on the topology architecture and routing of the constellation and the ephemeris of the satellite. The solutions for the pointing angles are uploaded to the spaceborne computer and executed. By comparing the in-orbit results and the calculation results, the performance of the pointing and tracking are validated. The review by [PERSON] et al. carried out recapture studies on inter-satellite laser links, considering a pointing error model of multipoint link terminals [24]. The results showed that subsequent research on inter-satellite links should optimize the scanning capture parameters of inter-satellite laser links. Current studies on the in-orbit test methods for inter-satellite links' performance highlight constellations that have been constructed. However, the construction of mega-constellations always takes several years [25; 26]. During the construction of the constellation, due to the loose distribution of the satellites, the distance and visibility between satellites might not satisfy the constraints for establishing an inter-satellite link [27]. Meanwhile, an inter-satellite link's performance should be tested in advance so that the construction of the constellation can be more flexible and confident. Therefore, the test method for a single satellite's pointing and tracking abilities has potential in practical missions. In this paper, a ground-station-based high-confidence test method for inter-satellite link pointing and tracking performances with respect to a single satellite is developed. During the construction of the constellation, due to the insufficiency of inter-satellite linking resources, the pointing and tracking abilities of the in-orbit satellite cannot be tested immediately. The ground station has the ability to construct a link with the in-orbit satellite, which can be employed to simulate the inter-satellite transmission. The test for a single satellite's pointing and tracking abilities involves using multiple ground stations. The contributions of this paper are summarized as follows: (1) A practical mission scenario for testing an inter-satellite link's performance is established. A local satellite and a target satellite are introduced as a signal projector and receiver, respectively. The motion of the beam of the local satellite during the tracking is described by the rotation angle and the off-axis angle. (2) A virtual target satellite for testing an inter-satellite link is proposed. The signal-receiving process of the virtual satellite is simulated by two ground stations. The orbit of the virtual satellite is analytically derived. The time difference between two transmissions with different ground stations is solved based on a Newton-Raphson method. (3) A test method for inter-satellite link pointing and tracking is proposed. Based on the virtual target satellite, the corresponding rotation angles, and off-axis angles with respect to the ground stations are obtained. During the inter-satellite link test, considering the time difference between ground stations receiving the signals from the local satellite, the inter-satellite link pointing and tracking abilities are evaluated. The rest of this paper is organized as follows: Section 2 presents the models of pointing vectors and pointing angles for establishing an inter-satellite link. In Section 3, the design method for a virtual target satellite via two ground stations is developed. The test method for inter-satellite link pointing and tracking is provided. The design of the virtual satellite and the test method for its pointing and tracking abilities are validated through numerical simulations in Section 4. Finally, Section 5 draws a conclusion of this paper.