# Extended Geometry and Probability Model for GNSS+ Constellation Performance Evaluation
## 4 Experimental Results and Analyses
### Bds-3 Vs Gps  
Using the EGAPM the performance of the BDS-3 and GPS constellations is analyzed from the aspects of satellite visibility, DOPs, correlations level between station height and receiver clock difference, and the ratio of positioning precision of longitude and latitude components. The results are shown in Figure 4 and Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Constellation**} & \multicolumn{4}{c}{**Underestimating Rates of DOPs (\%)**} \\  & \multicolumn{4}{c}{**Average (Min-Max)**} \\ \hline  & GDOP & PDOP & HDOP & VDOP \\ GPS & 10.41 (5.06–13.10) & 9.85 (4.58–12.40) & 7.98 (3.96–10.63) & 10.33 (4.64–13.03) \\ BDS-3+QZO & 10.94 (6.93–16.12) & 10.39 (6.46–15.09) & 7.95 (4.44–10.55) & 11.07 (6.79–16.91) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average, minimal, and maximal underestimating rates of the estimated GPS and BDS-3+QZO DOPs ((GDOP (geometric DOP), HDOP (horizontal DOP), PDOP (position DOP), TDOP (time DOP), and VDOP (vertical DOP) )) relative to the reference values ((reference-estimation)/reference \(\times\) 100%) over latitudes. Figure 3: Estimation and reference value of the number of visible satellites for 32 Global Positioning System (GPS) satellites and the BDS-3+QZO constellation at all latitudes (\(-90^{\circ}\) S–\(90^{\circ}\) N) for the cutoff elevation angle (CEA) of \(5^{\circ}\). (**a**) Estimation and reference value of the number of visible satellites for 32 GPS satellites; (**b**) Estimation and reference value of the numbers of visible satellites for BDS-3+QZO. Figure 4: Estimated DOPs (GDOP (geometric DOP), HDOP (horizontal DOP), PDOP (position DOP), TDOP (time DOP), and VDOP (vertical DOP) ), positioning precision in longitude versus latitude, and  
correlation between station height and receiver clock difference of the BDS-3 and GPS constellation with 5\({}^{\circ}\) CEA. (**a**) Number of visible satellites BDS-3; (**b**) Number of visible satellites GPS; (**c**) GDOP of BDS-3; (**d**) GDOP of GPS; (**e**) HDOP of BDS-3; (**f**) HDOP of GPS; (**g**) PDOP of BDS-3; (**h**) PDOP of GPS; (**i**) TDOP of BDS-3; (**j**) TDOP of GPS; (**k**) VDOP of BDS-3; (**l**) VDOP of GPS; (**m**) The ratio of positioning precision between the longitude component and the latitude component of BDS-3; (**n**) The ratio of positioning precision between the longitude component and the latitude component of GPS; (**o**) Correlation level between station height and receiver clock difference of BDS-3; (**p**) Correlation level between station height and receiver clock difference of GPS. From Figure 4a,b, we can find that the satellite visibility of GPS is more globally balanced than BDS-3, and for BDS-3, more satellites can be observed in the Asia-Pacific region while fewer satellites in the Western Hemisphere. From Figure 4c to Figure 4l, the DOPs of BDS-3 are larger than GPS in the Western Hemisphere. Note that VDOP is larger in high latitude regions, especially in the polar regions for both BDS-3 and GPS because, with an increase in station latitude, the elevation of satellites observed becomes lower. In this case, introducing HEO satellites into the GNSS constellation may make more satellites be observed, which might improve the geometry distribution in the vertical direction. As shown in Figure 4m,n, for the GPS constellation in most regions, the positioning precision in the longitude component is worse than for the latitude component. However, in contrast, for the BDS-3 constellation in some low latitude regions and some polar regions, the precision of the longitude component is better. The reason may be that GPS satellites are all MEO satellites, mainly flying along east-west direction so positioning precision is better in this direction. However, in the case of BDS-3, 3 IGSO satellites mainly fly along the longitude direction. Besides, the GEO satellites mainly contribute to DOP value in the longitude direction mainly [2].