# Precise Orbit Determination of BDS-2 and BDS-3 Using SLR
## 5 Discussion
### The Dependency on the Number of SLR Observations  
Figure 16 shows the dependency of RMS in RTN on the number of SLR observations. For GEO C01, the number of SLR observations can just reach 20 for the 3-day arc solutions and less than 40 for the 9-day arc solutions. For the three IGSO satellites, the maximum SLR observation number ranges from 30 to 90 for the 3-day to 9-day solutions of C08 and C10, while the number ranges from 60 to 140 for C13. Owing to its superiority of observation quantity, the SLR orbit determination accuracy of C13 is always better than that of C08 and C10 satellites under the same conditions. Similarly, the lack of observation quantity is an important factor leading to the poor accuracy of SLR-only orbit determination of C01. In five BDS MEO satellites, the number of SLR observations can be as many as 180 in the 9-day solutions of C11 satellite, followed by C21 as 140, and more than 100 for C20, C21, and C30. Overall, the dependency of median RMS on the number of SLR observations are similar for each satellite, whether it is a 3-, 5-, 7-, or 9-day solution.  
The accuracy increases and improves significantly when the number of SLR observations exceeds 50, especially in T and N directions. The dependency becomes stable and does not fluctuate greatly when the number of SLR observations reaches 80 or more. For the multi-day solution of individual satellites, the RMS of 7- or 9-day solutions are always better than that of 3- and 5-day solution when the number of SLR observations is in the range of 50 to 80, except for GEO C01. In addition, compared with the dependency of 3-day solutions RMS in RTN on the number of SLR observations for BDS-2 C08 and C11 by [PERSON], [PERSON] and Zajdel (2019), the similar dependency is reflected in Figure 16. The median RMS of 3-day solutions could still be unstable, even if the number of SLR observations reaches 80, especially in T and N directions, though the situation becomes optimistic in the 7- and 9-day solutions for BDS satellites. It indicates that the 7- and 9-day solutions are necessary for the SLR-only orbit determination of BDS satellites under the present conditions.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**PRN**} & \multicolumn{4}{c}{**Overlaps**} & \multicolumn{4}{c}{**Vs WUM**} \\ \cline{2-9}  & **R** & **T** & **N** & **3D-RMS** & **R** & **T** & **N** & **3D-RMS** \\ \hline
**C01** & 6.5 & 90.3 & 8.1 & 100.6 & 176.7 & 1796.1 & 367.5 & 2641.8 \\
**C08** & 15.4 & 135.3 & 111.3 & 185.8 & 19.0 & 133.5 & 116.8 & 207.5 \\
**C10** & 25.0 & 101.9 & 185.1 & 266.0 & 30.7 & 175.9 & 311.5 & 431.4 \\
**C13** & 16.9 & 58.4 & 78.0 & 114.4 & 21.6 & 82.1 & 81.1 & 130.1 \\
**C11** & 3.6 & 12.4 & 15.6 & 21.4 & 5.7 & 15.0 & 16.5 & 25.7 \\
**C20** & 5.7 & 21.6 & 23.4 & 33.3 & 9.0 & 27.2 & 27.2 & 45.8 \\
**C21** & 4.9 & 13.6 & 17.6 & 26.1 & 7.3 & 20.4 & 20.6 & 31.0 \\
**C29** & 4.8 & 17.5 & 20.7 & 31.4 & 9.6 & 36.8 & 35.2 & 57.9 \\
**C30** & 4.8 & 15.6 & 23.9 & 32.3 & 6.0 & 22.3 & 30.1 & 41.0 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The median RMS of 9-day solutions (Unit: cm).