## 3 Results
### Rnss + Four-Gnss
Particularly, in the area of (60\({}^{\circ}\)E-180\({}^{\circ}\)E, 60\({}^{\circ}\)S-60\({}^{\circ}\)N), that number increases to 50 or more. The maximal improvement rate of satellite visibility, compared to the four-GNSS-NG, reaches 15.7%, while the average is 7.6%. Adding 7-QZSS to the four-GNSS-NG reduces the GDOP by 18.0% on average, and that value ranges from 10.8% to 35% (average: 27%) in (60\({}^{\circ}\)E-180\({}^{\circ}\)E, 60\({}^{\circ}\)S-60\({}^{\circ}\)N). In general, the GDOP basically reduces to a value within 1.16, and the average is 0.95. For four-GNSS-NG+11-NavIC \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**System**} & \multirow{2}{*}{**Area**} & \multicolumn{2}{c}{**Ave.**} \\ \cline{3-4}  & & **Satellite** & **GODP** \\ \hline
7-QZSS & (60\({}^{\circ}\)E–180\({}^{\circ}\)E, 60\({}^{\circ}\)S–60\({}^{\circ}\)N) & 5.57 & - \\
11-NavIC & (30\({}^{\circ}\)E–150\({}^{\circ}\)E, 60\({}^{\circ}\)S–60\({}^{\circ}\)N) & 8.78 & - \\ four-GNSS-NG+7-QZSS & Eastern Hemisphere & 50.94 & 0.95 \\ four-GNSS-NG+11-NavIC & 53.80 & 0.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistical results of satellite visibility and GDOP for 7-QZSS, 11-NavIC, and their respective combination positioning with four-GNSS-NG results. Figure 12: Satellite visibility of QZSS and NavIC: (**a**) visible satellites of 4-QZSS; (**b**) visible satellites of 7-QZSS; (**c**) visible satellites of 7-NavIC; (**d**) visible satellites of 11-NavIC. combination positioning, the number visible satellites ranges from 43.93 to 65.00 (average: 53.80), with the exception of a small area in the extreme north India, more than 59 usable satellites are always visible over the entire Indian landmass. Ranging from 0.60 to 1.17, the GDOP of the four-GNSS-NG+11-NavIC is 0.86 on average in the Eastern Hemisphere, which is an improvement of 8.3-42.9% (average: 26.1%) compared to the four-GNSS-NG. Especially in India and Southeast Asia, the GDOP is less than 0.68, and the improvement rate is at least 34.0%. According to the four-GNSS and two RNSSs development programs, Figure 14 presents the satellite visibility and DOPs of the four-GNSS-NG+7-QZSS+11-NavIC on a global scale. The statistical results are listed in Table 8. The number of visible satellites is from 37.51 to 71.58 (average: 51.24). More satellites can be observed in the low altitudes of the Eastern Hemisphere and less in the areas of North and South America. Comparing to the operating satellites of four-GNSS+4-QZSS+7-NavIC, the satellite visibility improvement rate is from 11.6% to 32.0% (average: 21.1%). With more visible satellites, the PDOP, ranging from 0.50 to 1.08 (average: 0.82), improves by 12.8% on average. As shown in the illustration, the PDOP generally increases in the areas of (60\({}^{\circ}\)E-130\({}^{\circ}\)E, 30\({}^{\circ}\)S-30\({}^{\circ}\)N) towards the east and west ends. The maximum PDOP is at around 30\({}^{\circ}\) latitude in the Western Hemisphere. The HDOP and VDOP range from 0.37 to 0.56 (average: 0.46) and 0.32 to 0.94  
Figure 13: Satellite visibility and GDOP of the four-GNSS-NG+7-QZSS and the four-GNSS-NG+11-NavIC: (**a**) visible satellites of the four-GNSS-NG+7-QZSS; (**b**) GDOP of the four-GNSS-NG+7-QZSS; (**c**) visible satellites of the four-GNSS-NG+11-NavIC; (**d**) GDOP of the four-GNSS-NG+11-NavIC. (average: 0.67), respectively. Both of them are lower in the Asia-Pacific region. However, the HDOP is larger at 40\({}^{\circ}\leq|B|\leq\) 50\({}^{\circ}\), while VDOP is larger in (30\({}^{\circ}\)S\(\sim\)30\({}^{\circ}\)N) and in some high latitude areas. Figure 11e presents the ratio of NDOP/EDOP to explain the HDOP features. It can be seen that NDOP, which ranges from 0.26 to 0.44 (average: 0.34), is less than EDOP, which ranges from 0.27 to 0.38 (average: 0.34), in the areas of (30\({}^{\circ}\)S\(\sim\)30\({}^{\circ}\)N) and 75\({}^{\circ}\leq|B|\leq\) 90\({}^{\circ}\). Additionally, the east direction positioning accuracy is higher than that of the north in other areas.