# Autonomous Orbit Determination of LLO Satellite Using DRO-LLO Links and Lunar Laser Ranging
## 4 Autonomous Orbit Determination Simulation
### Autonomous Orbit Determination Results  
In the experimental data generation stage, reference orbits and measurement data are obtained. Then, the EKF is used for autonomous orbit determination and the estimated orbit is obtained. Finally, the estimated orbit is compared with the reference orbit to output position and velocity residuals. This article conducts three sets of numerical simulation experiments: 1 Experiment 1: tests the impact of lunar laser ranging data on the autonomous LiAISON orbit determination performance of the DRO-LLO; 2 Experiment 2: tests the impact of increasing initial error on the autonomous orbit determination performance of the DRO-LLO; and 3 Experiment 3: tests the impact of different dynamic model errors on the autonomous orbit determination performance of the DRO-LLO. The initial simulation settings for Experiment 1 are shown in Table 7. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Settings** \\ \hline Initial DRO/LLO position error/m & 1000 (\(1-\sigma\)) \\ Initial DRO/LLO velocity error/(m\(\cdot\)s\({}^{-1}\)) & 0.1 (\(1-\sigma\)) \\ Earth’s gravity & 70 \(\times\) 70 EGM2008 \\ Moon’s gravity & 50 \(\times\) 50 GL0660B \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Initial simulation settings for Experiment 1. Figure 6: Analysis of Cramér-Rao Lower Bound. Figure 9: LLO position residual. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Settings** \\ \hline Initial DRO/LLO position error/m & 10,000 (1\(-\sigma\)) \\ Initial DRO/LLO velocity error/(m\(\cdot\)s\({}^{-1}\)) & 1.0 (1\(-\sigma\)) \\ Earth’s gravity & 70 \(\times\) 70 EGM2008 \\ Moon’s gravity & 50 \(\times\) 50 GL0660B \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Initial simulation settings for Experiment 2. Figure 10: DRO position residual. accuracy of the LLO satellite has been improved from meters to decimeters, and the orbit determination accuracy of the DRO satellite has been improved from tens of meters to meters. As the number of corner reflectors increases, the convergence speed and orbit determination accuracy of satellites continue to improve. In summary, lunar laser ranging technology can improve the robustness of satellite orbit determination, ensuring the convergence speed and accuracy without considering dynamic model errors and increasing initial orbit errors. The initial simulation settings for Experiment 3 are shown in Table 9. The models of the non-spherical harmonic gravity fields of the Earth and the Moon have been matured, there is no need to analyze starting from the point-mass model [30; 31]. Therefore, an order of 30 is selected to simulate the errors of the dynamic model. Figures 11 and 12 present the autonomous orbit determination results of the DRO-LLO in Experiment 3. From Figures 11 and 12, the following can be concluded:  
Increasing the error of the dynamic model significantly reduces the convergence speed and accuracy of autonomous orbit determination relying solely on LiAISON; the orbit determination accuracy of the LLO satellite has decreased from decimeters to ten meters, and the orbit determination accuracy of the DRO satellite has decreased from tens of meters to hundreds of meters. Increasing lunar laser ranging data has improved the orbital convergence speed and accuracy of the DRO and LLO satellites. The orbit determination accuracy of the LLO satellite has been improved from tens of meters to meters, and the orbit determination accuracy of the DRO satellite has been improved from hundreds of meters to tens of meters. As the number of corner reflectors increases, the convergence speed and orbit determination accuracy of  
Figure 11: LLO position residual. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Settings** \\ \hline Initial DRO/LLO position error/m & 1000 (1\(-\sigma\)) \\ Initial DRO/LLO velocity error/(m\(\cdot\)s\({}^{-1}\)) & 0.1 (1\(-\sigma\)) \\ Earth’s gravity & 30 \(\times\) 30 EGM2008 \\ Moon’s gravity & 30 \(\times\) 30 GL0660B \\ \hline \hline \end{tabular}
\end{table}