## 5 Orbit Evaluation
### Slr  
SLR as a pivotal space technology enables the independent orbit accuracy validation of GNSS satellites. To facilitate SLR tracking, every BDS-3 MEO satellite is equipped with laser retroreflector arrays (LRA). Thus, we can carry out SLR validation for these BDS-3 MEO satellites. Since February 2023, ILRS SLR tracking mission has added all BDS-3 MEO satellites into its observation list [42]. In this study, SLR was employed to validate the orbits for BDS-3, excluding satellite C27 and satellite C28 as their SLR observations were not available. For reference, SLR validation was also applied to BDS-3 orbit products from CODE. Figure 10 exhibits the SLR validation results for 3-day arc orbits of BDS-3 MEO. The mean RMS of the BDS-3 satellite orbits from the BIC/B2a observations is 5.72 cm, slightly outperforming the B1I/B3I combination and CODE MGEX products. Most BDS-3 satellite orbits using SLR validation exhibit RMS values smaller than 6 cm. Only three satellites' orbit RMS values exceeded 8 cm, with satellite C44 having the largest RMS, reaching about 18 cm. The significant SLR residuals of C43 and C44 may be caused by the errors in the published metadata associated with the LRA [43]. The mean RMS of SLR validation for BDS-3 satellites' 3-day arc orbits, excluding C22, C43, and C44, is 4.47 cm for the B1I/B3I solution, 4.40 cm for the BIC/B2a solution, and 4.51 cm for the CODE solution, respectively. Among these three solutions, the BIC/B2a solution consistently demonstrates the best performance. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**RMS [cm]**} & \multirow{2}{*}{**Constellation**} & **Radial** & **Along** & **Cross** & **1D** \\  & & **Direction** & **Direction** & **Direction** & **Direction** \\ \hline \multicolumn{6}{l}{1-day arc} \\ \hline B1I/B3I & All & 3.01 & 3.54 & 2.66 & 3.09 \\  & IGSO & 7.02 & 5.42 & 4.32 & 5.70 \\  & MEO CAST & 2.00 & 3.05 & 2.48 & 2.55 \\  & MEO SECM & 1.83 & 3.38 & 2.17 & 2.55 \\ \hline BIC/B2a & All & 3.11 & 3.47 & 2.70 & 3.11 \\  & IGSO & 7.05 & 5.39 & 4.73 & 5.81 \\  & MEO CAST & 2.09 & 2.90 & 2.41 & 2.49 \\  & MEO SECM & 2.07 & 3.40 & 2.14 & 2.61 \\ \hline \multicolumn{6}{l}{3-day arc} \\ \hline B1I/B3I & All & 1.92 & 3.02 & 1.81 & 2.32 \\  & IGSO & 3.39 & 3.60 & 3.75 & 3.58 \\  & MEO CAST & 1.78 & 3.16 & 1.45 & 2.26 \\  & MEO SECM & 1.34 & 2.44 & 1.24 & 1.76 \\ \hline BIC/B2a & All & 1.94 & 3.04 & 1.89 & 2.35 \\  & IGSO & 3.50 & 3.70 & 3.97 & 3.73 \\  & MEO CAST & 1.79 & 3.16 & 1.50 & 2.27 \\  & MEO SECM & 1.31 & 2.48 & 1.28 & 1.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The RMS of 3-day arc orbit compared with CODE MGEX products for BDS-3 all satellites. The RMS values of SLR residuals for BDS-3 MEO orbits, obtained from B1I/B3I and B1C/B2a combination observations, including 1-day and 3-day arcs, along with CODE MGEX products, are exhibited in Table 8. Notably, the RMS values are slightly smaller for the 3-day arc orbits than those for the 1-day arc. For all BDS-3 orbits, the RMS value of the SLR residuals is 6.41 cm for the B1I/B3I solution, 6.39 cm for the B1C/B2a solution, and 6.38 cm for CODE MGEX products. It is essential to emphasize that the RMS values for BDS-3 MEO SECM SLR residuals are over 8 cm, which is more obvious than those of CAST satellites because of the larger residuals of SLR for satellites C43 and C44. Table 9 summarizes the RMS values of the SLR residuals for MEO satellite 3-day arc solutions, excluding satellites C22, C43, and C44, which have SLR residuals exceeding 8 cm. According to the statistics, the RMS values are 4.75 cm for the B1I/B3I solution, 4.69 cm for the B1C/B2a solution, and 4.70 cm for the CODE MGEX products. These results further emphasize that the B1C/B2a solution exhibits the best performance for the determination of the BDS-3 orbit.