## 5 Simulation and Analysis of Positioning Strategy of Constellation Station
### Simulation Scheme and Result Analysis of Relative Station-Position-Holding Strategy  
1. Setting of simulation conditions.  
Since relative phase control is more suitable for constellations with small numbers of satellites, the configuration of the low-orbit Walker constellation selected in the simulation test was 18/3/1, with an orbital altitude of 550 km and an orbital inclination of 53\({}^{\circ}\). The perturbation model of the simulation test was the Earth non-spherical \(J_{2}\) perturbation model, and the Jacchia 71 atmospheric density model (set) was used. The satellite surface-to-mass ratio was 0.01, the orbit forecast model was the HPOP model, and the range of the constellation phase-angle-deviation drift ring was maintained by the simulation analysis. The simulation phase-holding task period was 300 days, and \(C_{d}=2.2\).  
2. Simulation results.  
According to the evolution of the constellation configuration caused by the phase deviation drift, the nominal orbit of the constellation was taken as a reference, and the relative phase angle drift amounts of satellites 2\(-\)4 and 3\(-\)6 in low-solar-activity years were obtained. The main reason for the satellite phase angle drift shown in Figure 9 was that the semi-major axis of the orbit had an initial deviation from the nominal orbit. Therefore, the satellite phase angle showed nonlinear changes over time under the action of atmospheric drag.  
Figure 8: Time interval of phase\(-\)holding orbital maneuvering and change of semi\(-\)major axis of satellite 1.  
Figure 9: Relative phase angle drift amounts of satellites 2\(-\)4 and 3\(-\)6 in low\(-\)solar\(-\)activity years.  
According to the relative phase-maintenance strategy steps based on dynamic datum satellites, satellites 1\(-\)1, 1\(-\)2, 1\(-\)3, 2\(-\)1, \(\ldots\), and 3\(-\)3 were taken as the reference satellites, and the relative phase drift amounts of other satellites in the constellation were calculated. When satellite 1-2 was taken as the reference satellite, the total phase deviation beyond the critical threshold was the minimum, and the number of satellites to be controlled was the minimum.  
Table 5 shows the phase drift amounts of satellites in the constellation that exceeded the critical threshold of the phase deviation relative to reference star 1\(-\)2. Based on the statistical results and relative control process, satellite 1\(-\)2 was selected as the control reference, and orbit control was carried out on satellites 1\(-\)3, 2\(-\)2, 2\(-\)4, and 3\(-\)6. The results over 30 days after orbit control for the phase maintenance of the constellation satellites are shown in Figure 10. The phase angle deviation of satellite 2\(-\)4 relative to reference satellite 1\(-\)2 gradually decreased with time, and the change rate of the phase difference was about \(-\)0.0147\({}^{\circ}\). The phase angle deviation of satellite 3\(-\)6 relative to the reference star 1\(-\)2 gradually increased, and the phase difference change rate was about 0.0153\({}^{\circ}\).  
Based on the HPOP forecaster, orbit extrapolation and curve fitting were carried out on the satellite implementing orbit control. The changes in the satellite's relative phase angle to the reference star within 300 days were obtained, as shown in Figure 11. The simulation data showed that the phase angle drift amounts of all the satellites in the constellation were maintained within the range of \(\pm\)5\({}^{\circ}\) over 300 days, which was in line with the expectations.  
Figure 11: The variation of the phase angle of the satellite relative to the reference star with in 300 days.  
Figure 10: Phase angle drift of the satellite relative to the reference star after orbit control.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference Star** & **1\(-\)3** & **2\(-\)2** & **2\(-\)4** & **3\(-\)6** \\ \hline
1\(-\)2 & 4.35 & 4.13 & 4.38 & 4.37 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Relative phase drift amounts of satellites in the constellation with reference.