# Extended Geometry and Probability Model for GNSS+ Constellation Performance Evaluation
## 6 Conclusions  
Hybrid constellations will be one of the development trends in the future; hence, it is necessary to develop a simple strategy to evaluate the performance of GNSS+ constellations before these satellites are launched. We extend the previous GAPM, which is only suitable for circular orbits. Furthermore, most calculations of satellite visibility and DOPs are based on real or complex simulated ephemerides. However, our strategy estimates satellite visibility and DOPs based on a few orbital parameters of one satellite constellation. The features of the BDS-3 and GPS constellation were investigated. Satellite visibility of GPS is more balanced on a global scale than BDS-3. In contrast, for BDS-3, more satellites can be observed in the Asia-Pacific region and fewer satellites in the Western Hemisphere. VDOP is larger, especially in the polar regions for both BDS-3 and GPS. Furthermore, it is interesting to find that for the BDS-3 constellation, the precision in the longitude component is better in some low latitude and some polar regions, which are in contrast to GPS in these areas. Besides, the correlation level between station height and receiver clock difference is higher for both BDS-3 and GPS. For QZO satellites, their orbit's eccentricity is 0.075, and apogee is located above the Northern Hemisphere. Thus, these satellites stay a longer time above the Northern Hemisphere. Experiments show that when the BDS IGSO satellite is replaced by the QZO satellite, satellite visibility and GDOP are slightly better in the Northern Hemisphere but worse in the Southern Hemisphere relative to the BDS-3 constellation. HEO satellites are introduced to improve satellite visibility in high latitude regions. The performance of the BDS-3+HEO constellation is assessed, and results show that the geometric distribution in the middle and high latitude regions is significantly improved. It is worth noting that VDOP is decreased by 16.65%, and satellite visibility improved by 38.76% on average in the 30\({}^{\circ}\) N-90\({}^{\circ}\) N region. The performance of LEO satellites is also investigated, and the BDS-3+HEO+LEO constellation is analyzed. By introducing hundreds of LEO satellites, DOPs decreased greatly, 40% lower or so relative to the BDS-3 and GPS constellation on a global scale. In the meantime, it is interesting to find that the ratio of positioning precision between the longitude and the latitude component is strongly related to the direction of satellite travel. As LEO satellites are all at polar orbits, mainly flying along north-south \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Constellation** & **VisiNum** & **GDOP** & **HDOP** & **PDOP** & **TDOP** & **VDOP** \\ \hline BDS-3 & 197.81\% & 42.86\% & 43.59\% & 47.62\% & 49.32\% & 41.09\% \\ GPS & 183.99\% & 40.00\% & 41.33\% & 45.34\% & 46.38\% & 38.71\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Global average visible satellites and dilution of precision (DOP) values improving rates of BDS-3+HEO+LEO relative to BDS-3 and GPS. direction and experiment results reveal that positioning accuracy is better in the longitude component in most regions. The results and conclusion of this paper present a preliminary exploration for the design of the GNSS+ constellation and thus may benefit future GNSS development. [PERSON], [PERSON], and [PERSON] conceived and designed the experiments. [PERSON] performed the experiments and analyzed the data. [PERSON] and [PERSON] contributed analysis tools. [PERSON] wrote the paper. All authors have read and agreed to the published version of the manuscript. This work is mainly funded by the National Natural Science Foundation of China (No. 11673050); the Key Program of Special Development funds of Zhangjiang National Innovation Demonstration Zone (Grant No. ZJ2018-ZD-009); National Key R&D Program of China (No. 2018 YFB0504300); and the Key R&D Program of Guangdong province (No. 2018B030325001). The authors would like to thank the International GNSS service. The authors declare no conflicts of interest.