## 4 Results and Discussion
### Availability of BDS-3/BDS-2 Constellations  
We evaluate the global availability of BDS-3 and BDS-2 combined constellation in this section in terms of the PNT service rate, PDOP, and the number of visible satellites. We also present the results of the GPS constellation, for comparison. Our evaluation is based on the final precise satellite orbit products from Wuhan University (WHU) spanning one week (DOY 140-146 of 2020), which is approximately one repeat cycle for all types of BDS constellations (i.e., MEO/IGSO/GEO) and seven repeat cycles of GPS constellation. The real-time precise products from CNES are not employed due to their frequent interruption. It is important to note that the tracking satellites are identical for the CNES and WHU precise products in terms of BDS-3/BDS-2 and GPS. Thus, only those satellites supported by the CLK93 stream are included in the availability analysis. In this section, we just intend to carry out an optimal availability evaluation for the BDS-3/BDS-2 real-time PNT. The global regions are divided into 72 \(\times\) 72 grids every 2.5\({}^{\circ}\) in latitude and 5\({}^{\circ}\) in longitude, respectively. In each grid, it is considered that there is a virtual ground tracking station at the center. Following [PERSON] et al. [38], the altitude of the virtual stations is set to 25 m. The sampling interval is 15 min. The global maps for the number of visible satellites are shown in Figure 3. The maximum value for the maximum number and a minimum number of BDS-3/BDS-2 visible satellites is 23 and 17 in Asia-Pacific regions, respectively, and the corresponding minimum value is 9 and 3 in the Americas, respectively, as can be seen in Figure 3. The average number of BDS-3/BDS-2 visible satellites ranges from 6 to 19 on a global scale. The visible GPS satellites show a less regional difference compared to that of BDS-3/BDS-2, and for the maximum, minimum and average number of GPS satellites, the global varying range is 11-14, 5-9 and 8.8-10.7, respectively. The average satellite number of BDS-3/BDS-2 is 13-19 in the BDS-2 service regions (55\({}^{\circ}\) S-55\({}^{\circ}\) N latitude and 70\({}^{\circ}\) E-150\({}^{\circ}\) E longitude), while the  
Figure 2: Geographical distribution of stations used in the analysis. corresponding satellite number is 6-9.2 in the 0\({}^{\circ}\)-150\({}^{\circ}\) W longitude and 60\({}^{\circ}\) S-60\({}^{\circ}\) N latitude areas. Regarding these two geographical areas, we can observe 6.8 more BDS-3/BDS-2 satellites on average than GPS in the BDS-2 service area, but 2.6 less in the other one. Figure 4 exhibits the PNT service rate of GPS and BDS-3/BDS-2 during the analysis period (a week). The service rate refers to the percentage of the time, during which the PNT service is available for use, over the total time. When the PDOP value computed with at least four visible satellites is smaller than 30, the PNT service is considered to be feasible. We can see that both BDS-3/BDS-2 and GPS currently offer a nearly full-time PNT service, except for some American areas where the BDS-3/BDS-2 PNT service rate can decline to 97.6%. Figure 4: PNT service rate for BDS-3/BDS-2 and GPS on DOY 140–146 of 2020. Figure 3: Global maps of the maximum, minimum and average number of visible satellites of GPS and BDS-3/BDS-2 on DOY 140–146 of 2020 (note that a visible satellite has an elevation angle higher than 7\({}^{\circ}\)). Figure 5 provides the global maps of the PDOP values. Only the results at the time spans when the PNT service is considered to be feasible are used for the statistics. Corresponding to the satellite visibility, the PDOP values of BDS-3/BDS-2 also demonstrate the viewable regional difference. The minimum value of the maximum and minimum BDS-3/BDS-2 PDOP values is respectively 1.5 and 0.9 in Asia-Pacific regions, and the corresponding maximum value is respectively 30.0 and 1.8 in Americas, resulting in an average PDOP that is 0.4 smaller in Asia-Pacific areas, but 1.0 larger in Americas with respect to that of GPS.