## 4 Results
### BDS2-Based Precise Relative Orbit Determination (PROD)  
As BDS2 is a regional navigation satellite system, the amount of BDS2 observations was much less than that of GPS. The carrier phase tracking arcs from TH-2A and TH-2B satellites on DOY 305 in 2019 are displayed in Figure 7, where the color bar represents the elevation and the red dashed lines indicate the center of burn time. The average of continuous tracking arcs was 410 for GPS satellites, while that it was only 179 for BDS2 satellites. The average duration of continuous tracking arcs was 31.5 min, while it was only 26.2 min for BDS2 satellites. Therefore, for the BDS2-based PROD we excluded the time intervals for each day from midnight to 1 h after the third maneuver. In addition, considering the small number of BDS2 observations, the threshold for the number of visible satellites was reduced from 3 to 2, and the threshold for the duration of continuous tracking arc was reduced from 400 s to 200 s. The piecewise periodic empirical accelerations in T and N directions were estimated every 3 h.  
Due to the worse ephemeris and poor geometry of GEOs [39; 40], three different weighting strategies were designed to analyze the effect of GEOs on PROD. The IGSOs  
Figure 7: Duration and common elevation of continuous carrier phase tracking arcs for navigation satellites of the two TH-2 satellites: (**a**) GPS satellites; (**b**) BDS2 satellites.  
and MEOs were treated as unit weight and the weight of GEOs was relative to the IGSOs and MEOs. Figure 8 and Table 3 show the difference between the GPS-based PROD and BDS2-based PROD in the R, T, and N directions with the different weight of GEOs. The differences increased with the decrease in the GEOs' weight. The average value of the daily RMS differed between the GPS-based and BDS2-based PROD. The average value of the daily RMS was 7.08 mm, 8.00 mm and 11.40 mm in 3D (global) when the weight of GEOs was 1, 0.5, and 0.2, respectively. The results showed that GEO satellites play important roles when BDS2 are applied to the PROD of LEO satellite formation. The relative position between TH-2A and TH-2B is only a few hundred meters, and the influence of ephemeris errors on PROD can be ignored, which agrees with [PERSON] et al. [17]. It can be concluded that the accuracy of BDS2-based PROD can reach millimeter-level. In the following analysis, the MEOs, IGSOs, and GEOs are treated as equal weight.  
Considering that BDS2 is a regional constellation, the difference in the accuracy of PROD in different regions needs to be analyzed. The spatial distribution of difference between the GPS-based and BDS2-based PROD in 3D is presented in Figure 9, the mean 3D accuracy of each 5\({}^{\circ}\)\(\times\) 5\({}^{\circ}\) zone was calculated. The accuracies of BDS2-based PROD in different regions were apparently different. The Asia-Pacific region was defined as longitudes from 55\({}^{\circ}\) E to 180\({}^{\circ}\) E and latitudes from 55\({}^{\circ}\) S to 55\({}^{\circ}\) N. The RMS values of difference between the GPS-based and BDS2-based PROD in the Asia-Pacific region and non-Asia-Pacific region were 2.89 mm and 7.96 mm, respectively. The results are basically consistent with [PERSON] et al. [15]. There were some arcs with large residuals in Figure 7, which  
Figure 8: Difference between the GPS-based and BDS2-based PROD with different weights of GEOs (excluding maneuver periods).  
were caused by the failure of integer ambiguity resolution. The ambiguity fixed rate was only 92.6% based on BDS2-only. The main reason is that there are not enough observations in some batches to ensure the ambiguities were estimated correctly. The average number of ambiguities was 11.6 per processing batch based on GPS-only, while it was only 5.0 for BDS2-only.