## 5 Conclusions  
Bedou-3 innovatively achieves autonomous navigation through inter-satellite links. However, current issues still exist, such as the overall constellation rotation and the limitation of orbital accuracy by prior constraints. In recent years, SLR observations have been gradually made public. Thanks to their significant advantages of high precision and no ambiguous parameters, they can be introduced into autonomous navigation for joint orbit determination, providing new ideas for solving existing problems. This paper focuses  
Figure 10: RMS before and after Helmert transformation of SLR/SLR orbit determination using broadcast ephemeris (**right**) and precision ephemeris (**left**) as a priori orbits. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{4}{c}{**IGSO**} & \multicolumn{4}{c}{**MEO**} \\  & **Along** & \multicolumn{2}{c}{**Cross**} & \multicolumn{2}{c}{**Radial**} & \multicolumn{2}{c}{**Along**} & \multicolumn{2}{c}{**Cross**} & \multicolumn{2}{c}{**Radial**} \\  & **Before** & **After** & **Before** & **After** & **Before** & **After** & **Before** & **After** & **Before** & **After** & **Before** & **After** \\ \hline brdc & 73.6 & 15.7 & 84.6 & 10.6 & 25 & 19.5 & 39.2 & 9.9 & 50.6 & 7.2 & 5.8 & 4.7 \\ prec & 30.5 & 16 & 27.3 & 11 & 23.9 & 19.4 & 10.4 & 9 & 16 & 7 & 5 & 4.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Average RMS in all directions of the orbit of the BDS-3 satellite (cm). on analyzing the impacts of different prior orbital constraints and different observation data on the orbit determination accuracy and the constellation translation. Firstly, a mathematical model for orbit determination by combining ISL after introducing SLR is derived. Subsequently, experiments are carried out and evaluated using one month of actual ISL and SLR observation data. The results show the following:  
1. There is good consistency across different days. Compared with using broadcast ephemeris as prior constraints, using precise ephemeris as prior constraints shows better consistency;
2. The accuracy of prior orbits affects the performance of the orbit determination. Compared with using broadcast ephemeris as prior constraints, using precise ephemeris as prior constraints can improve the orbital accuracy by approximately 75%;
3. The type of observation data affects the performance of orbit determination. Introducing SLR observations for joint orbit determination with ISL can improve the orbital accuracy by 13% to 26%. In addition, the improvement range for MEO satellites is larger than that for IGSO satellites;
4. Regardless of whether broadcast ephemeris or precise ephemeris is used as prior constraints, constellation translation and rotation still exist, and the results of the former are more obvious. Among the seven estimated parameters, for translation parameters, TX is the largest, followed by TY, and TZ is the smallest; for rotation parameters (such as RX, RY, and RZ), all show relatively large values, which may be related to the limited number of available satellite laser ranging stations during this period;
5. After considering constellation translation and rotation, the orbital accuracy under different prior constraints remains at the same level. The RMS shows that the orbital accuracy of the IGSO satellites in three directions is better than 20 cm, while the accuracy of the MEO satellites in along-track, cross-track, and radial directions is better than 10 cm, 8 cm, and 5 cm, respectively. [PERSON] conceived the idea and designed the experiments with [PERSON]; [PERSON], [PERSON] and [PERSON] organized and analyzed the data; [PERSON] checked the data. All authors participated in writing and revising this paper. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China under Grant U20A0193. Data Availability StatementData related to this article are available upon request to the corresponding author.