## 3 Results and Analysis
### Combination of GPS, GLONASS, and BDS for PPP Solutions
#### 3.2.1 Ambiguity-Float PPP Solution
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**STD (cm)**} & \multicolumn{3}{c}{**RMS (cm)**} \\ \cline{2-7}
**TYPE** & **E** & **N** & **U** & **E** & **N** & **U** \\ \hline GPS & 1.32 & 0.63 & 1.69 & 1.64 & 0.81 & 1.98 \\ GPS + B & 1.11 & 0.60 & 1.63 & 1.39 & 0.78 & 1.97 \\ GPS + R & 1.01 & 0.56 & 1.55 & 1.29 & 0.76 & 1.87 \\ GPS + RIM & 0.84 & 0.53 & 1.32 & 1.16 & 0.73 & 1.69 \\ GPS + G & 1.31 & 0.66 & 1.75 & 1.60 & 0.83 & 2.02 \\ GPS + I & 0.98 & 0.57 & 1.57 & 1.29 & 0.77 & 1.93 \\ GPS + M & 1.26 & 0.61 & 1.67 & 1.57 & 0.80 & 1.96 \\ GPS + GI & 1.12 & 0.61 & 1.68 & 1.41 & 0.79 & 2.00 \\ GPS + GM & 1.30 & 0.64 & 1.72 & 1.58 & 0.83 & 2.01 \\ GPS + IM & 1.01 & 0.57 & 1.59 & 1.30 & 0.77 & 1.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Position error statistics of convergent static GPS ambiguity-float PPP solutions for all 20 sites. and all different combined solutions. Similar as that of static PPP, the inclusion of any single type of BDS satellites to GPS PPP (_i.e._, GPS + I, GPS + M, GPS + G solutions) accelerates the convergence, and the GPS + I solutions converge fastest among three solutions. However, once GEO satellites are introduced to GPS + I or GPS + IM solutions, the averaged convergence time of GPS + GI and GPS + B solution slightly increase. The averaged convergence time is 46.64 min for GPS only PPP, whereas only 25.44 min, 20.69 min and 16.80 min for GPS + B, GPS + R, and GPS + RIM solutions, respectively. It is reduced significantly by 45.5%, 55.6% and 64.0%, thanks to the significant enhancement of geometric strength and redundancy by extra satellites in kinematic mode. As for the statistics of positioning errors listed in Table 6, it can be seen that the BDS IGSO contributes most to the positioning accuracy among three kinds of BDS satellites by the comparison of GPS + G, GPS + I, and GPS + M solutions. Furthermore, the positioning accuracy could also be contaminated slightly by inclusion of GEO satellites to GPS and IGSO combined PPP solutions, _i.e._, GPS + I and GPS + IM. Those results confirm the conclusion drawn from the static PPP solutions. The accuracy improvement in the vertical direction by combination of GLONASS and GPS is greater than that of BDS and GPS combined solution, whereas similar accuracy in horizontal direction has been achieved for GPS + R and GPS + IM solution. Finally, the GPS + RIM solution has the fastest convergence speed and highest positioning accuracy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**TYPE**} & \multicolumn{3}{c}{**STD (cm)**} & \multicolumn{3}{c}{**RMS (cm)**} \\ \cline{2-7}  & **E** & **N** & **U** & **E** & **N** & **U** \\ \hline GPS & 1.87 & 1.08 & 2.59 & 2.38 & 1.27 & 3.00 \\ GPS + B & 1.17 & 0.77 & 2.20 & 1.66 & 0.99 & 2.71 \\ GPS + R & 1.03 & 0.69 & 1.86 & 1.44 & 0.89 & 2.22 \\ GPS + RIM & 0.86 & 0.61 & 1.71 & 1.23 & 0.83 & 2.13 \\ GPS + G & 1.67 & 0.96 & 2.52 & 2.21 & 1.16 & 2.90 \\ GPS + I & 1.09 & 0.78 & 2.01 & 1.53 & 0.98 & 2.51 \\ GPS + M & 1.72 & 1.01 & 2.45 & 2.23 & 1.19 & 2.87 \\ GPS + GI & 1.22 & 0.81 & 2.25 & 1.72 & 1.03 & 2.77 \\ GPS + GM & 1.61 & 0.93 & 2.46 & 2.15 & 1.12 & 2.84 \\ GPS + IM & 1.04 & 0.74 & 1.94 & 1.47 & 0.95 & 2.43 \\ \hline \end{tabular}
\end{table} 
Table 6: Position error statistics of convergent kinematic ambiguity-float PPP solutions for all 20 sites. Figure 5: Statistics of convergence time in each 10 min and the averaged convergence time of the kinematic ambiguity-float PPP solutions for all sites.