## 4 Precise Orbit Determination (POD)
### Orbit Validation  
#### 4.2.1 Orbit Overlap Comparisons  
Orbit overlap comparisons are widely used to validate the internal consistency of orbits, which can evaluate precision at each epoch in overlapped time of the orbit. Thus, the method based on the overlap between two adjacent arcs is utilized in this study. We compared the satellite positions on the middle day of the first three-day arc and the first day of the second arc. As mentioned above, data from DOY 021 to DOY 079 in 2017 were considered in this study. Table 5 shows the RMS results of an overlap comparison of the real-valued ambiguity solution. As listed in Table 5, the results of the orbit comparison of BeiDou-2 and BeiDou-3e IGSOs and MEOs were on the same scale: the radial component was about 4.3-6.5 cm, the cross-track component was about 11.5-19.4 cm, and the along-track component, which was the largest, was approximately 13.4-21.5 cm. The three-dimensional RMS value was about 19.7-27.4 cm. Owing to poor geometry, the RMS value of the along-track component was about 46.6-73.4 cm for GEOs, which was much larger than those for IGSOs and MEOs, but the cross-track component was about 3.2-8.0 cm, which was much smaller than those for IGSOs and MEOs. The radial component was about 6.0 cm and was thus on the same scale as those for IGSOs and MEOs. In this study, the ambiguity was not fixed for GEOs owing to their poor geometry, but the performance of IGSOs and MEOs was still inspiring, and our results showed that the ambiguity fixing \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**PCO**} \\ \cline{2-4}  & **X** & **Y** & **Z** \\ \hline
**C31** & \(-5\) & \(0\) & \(100\) \\
**C32** & \(-4.5\) & \(-30\) & \(250\) \\
**C33** & \(-20\) & \(0\) & \(150\) \\
**C34** & \(-20\) & \(0\) & \(150\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PCO values for BeiDou-3e satellites (cm). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Satellite Type** & **PRN** & **Along-Track** & **Cross-Track** & **Radial** & **3D** \\ \hline \multirow{6}{*}{BeiDou-2 GEO} & C01 & 46.6 & 4.3 & 5.5 & 47.1 \\  & C02 & 51.8 & 4.7 & 6.0 & 52.4 \\  & C03 & 61.1 & 3.2 & 5.7 & 61.4 \\  & C04 & 71.7 & 6.7 & 5.8 & 72.2 \\  & C05 & 73.4 & 8.0 & 7.6 & 74.2 \\ \hline \multirow{6}{*}{BeiDou-2 ICSO} & C06 & 13.4 & 19.4 & 5.1 & 24.1 \\  & C07 & 14.0 & 13.2 & 4.8 & 19.9 \\  & C08 & 14.8 & 15.5 & 4.8 & 21.9 \\  & C09 & 15.5 & 18.7 & 5.4 & 24.9 \\  & C10 & 14.8 & 13.3 & 4.4 & 20.4 \\  & C13 & 14.9 & 16.9 & 4.8 & 23.0 \\ \hline \multirow{6}{*}{BeiDou-2 MEO} & C11 & 17.3 & 12.8 & 4.8 & 22.0 \\  & C12 & 15.5 & 11.5 & 4.3 & 19.7 \\  & C14 & 15.6 & 11.6 & 4.9 & 20.0 \\ \hline \multirow{2}{*}{BeiDou-3e IGSO} & C31 & 21.5 & 15.7 & 6.5 & 27.4 \\  & C32 & 16.9 & 15.1 & 5.5 & 23.3 \\ \hline \multirow{2}{*}{BeiDou-3e MEO} & C33 & 17.1 & 12.3 & 4.8 & 21.6 \\  & C34 & 20.2 & 15.1 & 5.5 & 25.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of overlap comparison of real-valued ambiguity solution for BeiDou-2 and BeiDou-3e satellites in along-track, cross-track, radial and three-dimensional (3D) directions (cm). Pseudo random noise (PRN). rate for IGSOs and MEOs was about 80%. The comparative results for BeiDou-2 and BeiDou-3e satellites before and after successful fixing are shown in Figure 5. As depicted in Figure 5, all the radial components were enhanced very slightly, but the along-track and cross-track components were enhanced by almost 10% for IGSOs. The performance of MEOs improved to a less extent than that of IGSOs, and some satellites were even worse than that of real-valued ambiguity solution, which may be due to the large tracking gap occurred in MEOs when they were outside the Asia-Pacific zone, as shown by the locations of the tracking stations in Figure 1. It should be noteworthy that continuous observation can be achieved only for IGSOs, but not for MEOs, which results in lower precision of parameters for MEO, compared with that for IGSO. Owing to discontinuous observation for MEOs, poor orbit precision of MEOs was displayed.