# Test Method for Single Satellite's Inter-Satellite Link Pointing and Tracking via Ground Station
## 3 Inter-Satellite Links Pointing and Tracking in-Orbit Test Method  
### Test Method for Single Satellite's Inter-Satellite Link Pointing and Tracking  
In order to validate the performance of the inter-satellite link in the current test method, the local satellite points and tracks an in-orbit target satellite. However, during the construction of the constellation, the distribution of the satellites might not satisfy the constraints for testing the inter-satellite link. In the present paper, an indirect test method for inter-satellite link pointing and tracking based on ground stations and a virtual satellite is developed. This indirect test process is shown in Figure 2.  
Figure 1: Definition of the link beam pointing angle. \(\gamma_{oa}\) denotes the off-axis angle; \(\gamma_{ra}\) denotes the rotation angle. Due to the lack of an in-orbit target satellite, the ground stations are introduced to simulate the positions of the virtual target satellite. The ground stations have capacities for receiving signals from the local satellite and calculating the time difference in signal reception between the two ground stations. Therefore, by pointing and tracking two ground stations, the local satellite indirectly validates the process of tracking the target satellite. In this situation, the corresponding orbit of the virtual target satellite is generated according to the visibilities between the local satellite and the ground stations. A detailed design method for the virtual satellite is provided in Section 3.2. Based on the ground station and the virtual satellite, the basic flow of the indirect test method is shown in Figure 3. The test method for inter-satellite link pointing and tracking is divided into the following steps:  
1. Choose two ground stations: A and B. Set time \(t_{1}\) when the local satellite points to ground station A, according to practical requirements. Then, propagate the positions of the ground stations \(\mathbf{r}_{d}\) at time \(t_{1}\);
2. Calculate the position of the local satellite \(\mathbf{r}_{s}\) and the relative positions between the local satellite and the ground stations \(\mathbf{r}_{dAs}\), \(\mathbf{r}_{dBs}\). The positions \(\mathbf{r}_{A}(t_{1})\) and \(\mathbf{r}_{B}(t_{1})\) of the virtual target satellites with respect to ground stations A and B, respectively, are obtained at time \(t_{1}\);
3. Calculate the time \(t_{2}\) when the local satellite points to ground station B and the corresponding position \(\mathbf{r}_{B}(t_{2})\) of the virtual target satellite, based on a Newton iteration method. The time difference between pointing to ground stations A and B is obtained. A detailed method is provided in Section 3.3;
4. Calculate the velocity of the virtual target satellite \(\mathbf{v}_{A}\). The orbit of the virtual target satellite is obtained. A detailed calculation method is provided in Section 3.4;
5. Predict the time difference between two ground stations receiving the signals from the local satellite. Then, the pointing and tracking of the local satellite with respect to the ground stations is executed in-orbit. The actual time difference is also obtained. By comparing the actual time difference and predicted time difference, the inter-satellite link pointing and tracking abilities of the local satellite are verified. Moreover, in order to test the inter-satellite link pointing and tracking performance, the virtual satellite should be similar to a practical satellite. Therefore, taking a practical constellation as a reference, the orbital altitude \(h_{0}\) of the virtual target satellite is set the same as the practical satellite to establish the inter-satellite link. The eccentricity is set as 0. Other orbital elements, including the right ascension of the ascending node, the argument of perigee, and the true anomaly, are solved by iterating steps (3)-(4). The orbital period of the virtual target satellite is denoted as \(T_{o}\).