## 3 Results
### BDS3 Joint POD Results Based on Ground Monitoring Stations and ISL
The 24 MEO satellites adopt the Walker: 24/3/1 constellation configuration, have an orbital radius of 27,906 km, and are evenly distributed in 3 orbital planes with 120 degrees of difference in equatorial longitude from the ascending node [1], as shown in Table 3. Figure 2 shows the BDS-3 satellites' ground-tracks. \begin{table}
\begin{tabular}{c c c c} \hline
**GNSS** & \multicolumn{3}{c}{**BDS-3 Satellites**} \\ \hline
**Orbit Type** & **GEO** & **IGSO** & **MEO** \\ \hline Satellites number & 3 & 3 & 24 \\ \hline Pseudo-random noise (PRN) number & C01, C02, C03 & C04, C05, C06 & C07–C30 \\ \hline Altitude & 35,786 km & 35,786 km & 21,528 km \\ \hline Inclination & 0\({}^{\circ}\) & 55\({}^{\circ}\) & 55\({}^{\circ}\) \\ \hline Constellation &
\begin{tabular}{c} Located at 80\({}^{\circ}\)E, \\ 110.5\({}^{\circ}\)E, and 140\({}^{\circ}\)E \\ \end{tabular} & RAAN of 118\({}^{\circ}\)E & Walker (24/3/1) \\ \hline \end{tabular}
\end{table} 
Table 3: Nominal constellation configuration of BDS-3. Figure 1: Distribution of the 7 ground monitoring stations. A satellite orbit assessment uses the difference between the calculated navigation satellite orbit and the real orbit to count the RMS value of the orbit difference in the along-track, cross-track, radial (A, C, R), and three-dimensional (3D) directions of the BDS-3 satellites' orbit [10]. Figure 3 shows the effective values of seven sta and seven sta and ISL in the 3D RMS, using both schemes for POD and time synchronization experiments. It can be seen that the average orbit accuracy of all BDS-3 satellites is 0.748 m without ISL data. The seven sta and ISL scheme has an average orbital accuracy of 0.035 m. The use of ISL data resulted in a high orbit accuracy for BDS-3, with an improvement of about 96.1% compared to the seven sta schemes. The addition of ISL data can make up for the lack of the number and distribution of ground-monitoring stations, improve the tracking of geometric observation shape changes, and make the satellite geometry more robust [40]. Figures 4 and 5 show the RMS in the A, C, and R direction for the seven sta and seven sta and ISL schemes, respectively. The average RMS of all BDS-3 satellites in the seven  
Figure 3: RMS in 3D direction for both 7 sta and 7 sta and ISL schemes. Figure 2: BDS-3 constellation navigation subastral point ground-tracks diagram. sta scheme were 0.679 m, 0.231 m, and 0.152 m in the A, C, and R directions, respectively, while the average RMS for all BDS-3 satellites in the seven sta and ISL scheme is 0.025 m in the along direction, 0.022 m in the cross direction, and 0.005 m in the radial direction. The seven sta and ISL scheme improves 96.3%, 90.5%, and 96.8% in the A, C, and R directions compared to the seven sta scheme [40]. The satellite clock offset accuracy assessment method uses the second difference comparison method [41; 42]. To begin with, the C01 satellite is designated as the reference clock. The clock offset outcomes obtained from other satellites are then referenced to this clock, thereby eliminating any differences in clock offset caused by contrasting reference clocks. Finally, a double difference comparison is conducted between the obtained results. The RMS1 and RMS2 of the statistical quadratic difference time series are given by Equation (27):  
\[RMS1=\sqrt{\left(\sum_{i=1}^{n}\Delta_{i}\Delta_{i}\right)/n},\ RMS2=\sqrt{ \left(\sum_{i=1}^{n}\left(\Delta_{i}-\overline{\Delta}\right)(\Delta_{i}- \overline{\Delta})\right)/n} \tag{27}\]  
Figure 4: The 7 sta scheme BDS-3 constellation in A, C, and R directions of RMS. Figure 5: The 7 sta and ISL scheme BDS-3 constellation in A, C, and R directions of RMS. where \(\Delta_{i}\) is the quadratic difference at the epochs and \(\overline{\Delta}\) is its average value. RMS1 and RMS2 are the roots mean square and standard deviation of the second difference time series [43]. As shown in Figures 6 and 7, using the seven sta scheme, the average accuracy of RMS1 for all satellites of BDS-3 is 0.89 ns, and the average accuracy of RMS2 is 0.83 ns, respectively.