## 3 Results  
### Four-GNSS  
Detailed characteristics of the four-GNSS constellations are given in Table 1. According to the satellite observation probability estimation methodology, we derived the \(\kappa\) of the four-GNSS MEO satellites, which are list in Table 1. Then, the \(P_{M}(\lambda_{i},\phi_{j})\) of the four-GNSS MEO satellites were calculated. The results are presented in Figure 1. Moreover, 12 Galileo 2 nd Generation satellites will join the existing constellation [13; 14]. In the future, there will be 36 Galileo satellites int space to provide global services. Hence, the results of the full Galileo constellation are also shown in Table 1 and Figure 1. The satellite observation probability of BDS-3M is similar to that of the 24-satellite Galileo constellation and is less than that of the GPS and the 36-satellite Galileo constellation because there are fewer MEO satellites in BDS-3. With the largest orbit inclination, GLONASS satellites cover a wider range of latitudes, which disperses the probability of latitudinal distribution and results in a minimum observation probability compared to the other systems. Based on the observation probability, the satellite visibility and the DOPs of four-GNSS and their next-generation constellations are estimated and analyzed in the following paragraph. Figure 1: Distribution the observation probabilities of the GPS (32-satellite), BDS-3 MEO (BDS-3M 24-satellite), Galileo (24-satellite, and 36-satellite), and GLONASS (24-satellite) satellites. BDS-3 adopts a heterogeneous constellation design and comprehensively completes deployment [9]. For future development, [PERSON] et al. [10] provided several suggestions, one of which was to increase the inclination of IGSO satellites to improve the navigation services in the Arctic region for scientific research and transportation. Based on the observation probability of IGSO satellites \(P_{I}(\lambda_{i},\phi_{j})\), we derived the average elevation angle \(\overline{E}_{I}\) of the IGSO satellites through Equation (16):  
\[\overline{E}_{I}=\sum P_{I}(\lambda_{i},\phi_{j})\cdot E_{ij}/\sum P_{I}( \lambda_{i},\phi_{j}) \tag{16}\]  
where \(E_{ij}\) is the elevation angle of a satellite on the grid \((\lambda_{i},\phi_{j})\). The \(\overline{E}_{I}\) of the IGSO constellations with 55\({}^{\circ}\), 60\({}^{\circ}\), 65\({}^{\circ}\), 70\({}^{\circ}\), and 75\({}^{\circ}\) inclinations are presented in Table 2. It can be seen that with the nominal constellation parameters of BDS-3I, the average elevation angle is 31.02 at high latitudes (75\({}^{\circ}\leq|B|\leq 90^{\circ}\)) in the Eastern Hemisphere. The improvement rate of the average elevation angle is approximately 7% when the inclination of the IGSO is increased by 5\({}^{\circ}\). The average elevation angle reaches 40.06\({}^{\circ}\) when the inclination of 3 BDS-3I increases to 75\({}^{\circ}\). To assess the performance of BDS-3 by adjusting the inclination of BDS-3I from 55\({}^{\circ}\) (BDS-3-nominal) to 75\({}^{\circ}\) (BDS-3-simulation), satellite visibility and GDOP were calculated. The results are shown in Figure 2 and Table 3. The number of visible BDS-3-nominal satellites ranges from 7 to 15 (average: 10.46), which is almost the same as that of the BDS-3-simulation (average: 10.49). Specifically, in the Asia-Pacific region, more than 12 satellites can be observed. The GDOP for both is less than 2.4. As the BDS-3I inclination increases, the GDOP decreases by approximately 3.8-8.0% (average: 6.9%) in the high-latitude region, while that in the high latitudes of the Eastern Hemisphere, the GDOP is 7.2% on average. It is clear that the BDS-3-simulation constellation can improve the geometric distribution of satellites in the Arctic region.