## 3 Results and Analysis
### Combination of GPS, GLONASS, and BDS for PPP Solutions
#### 3.2.1 Ambiguity-Float PPP Solution  
In this section, the impacts of BDS and GLONASS observations on the GPS ambiguity-float PPP are analyzed. Figure 4 demonstrates the percentage of convergence sessions in each 10 min period and the averaged convergence time for all static solutions computed from the aforementioned sites. As can be seen, different with that of BDS only static PPP, the convergence time is shorter, ranging from 0 to 50 min for most GPS only PPP solutions (about 95%). Only in occasional cases, when the solutions suffer from relatively few GPS satellites or bad data quality, the convergence time is longer than 50 min. Compared to the GPS only solution, the inclusion of any single type of BDS satellites accelerates the convergence speed to 22.81 min, 19.26 min and 22.88 min from 24.64 min for GPS + G, GPS + I, and GPS + M solutions, respectively. Again, IGSO satellites make the largest reduction to the convergence time. Compared the averaged convergence times of GPS + I solutions with that of GPS + GI, and GPS + B with GPS + IM solutions, it can be seen that the averaged convergence time become slightly longer after adding the GEO satellites. This indicates that GEO satellites might have the potential to slow the convergence speed of the GPS combined static PPP solutions once the IGSO observations are also used. However, the contamination is rather minor, at least with the strategy used in this contribution. On the other hand, once the GLONASS or BDS observations are combined with GPS, almost all PPP sessions are converged in 50 min thanks to better observation condition. The averaged convergence time is 24.64 min for GPS only PPP, while it is 18.97 min and 15.85 min for G + B and G + R solutions, respectively. However, only 1.91 min has been reduced when BDS IGSO and MEO are added in GPS and GLONASS combined PPP. Hence, those demonstrate that GLONASS makes larger reduction to the convergence time of GPS based combined PPP solutions than that of BDS,but the combination of the three GNSS systems could obtain the shortest convergence time among all these solutions. Table 5 lists the statistics of positioning errors of all static PPP solutions computed from 20 sites. It can be seen that the positioning accuracy in each component is improved after adding either IGSO or MEO satellites to the PPP solutions. Although the accuracy in the east component is improved when GEO observables are combined with GPS data for PPP, it decreases slightly in other two directions. When we compare the position errors of GPS + I solutions with that of GPS + GI ones and GPS + B with GPS + IM solutions, it can be found that the positioning errors in each component become slightly larger after adding the GEO satellites. These are similar as that of convergence time. This indicates that GEO satellites also have the potential to contaminate the accuracy of the GPS and BDS IGSO combined static PPP solutions slightly. Compared the GPS + R solutions and GPS + I or GPS + IM solution, which are the best GPS and BDS combined solutions, it seems that the accuracy improvement in the vertical direction by inclusion of GLONASS observations is still larger than that of BDS. For other two components, BDS IGSO and MEO satellites make similar contribution to the accuracy as GLONASS satellites do. The GPS + RIM solution has the highest positioning accuracy among these ten solutions, while the accuracy improvement w.r.t GPS + R is mainly in the horizontal direction. For kinematic ambiguity-float PPP, the corresponding statistic results for convergence time are plotted in Figure 5. Due to the fact that position parameters are estimated in epoch-wise, the averaged convergence time of kinematic PPP is significantly longer than that of static PPP for both GPS only  
Figure 4: Statistics of convergence time in each 10 min and the averaged convergence time for the static ambiguity-float PPP solutions of all sites.