## 3 Results
### Positioning Performance of the Dual Systems  
The three dual-system schemes are compared to their corresponding single-system schemes in the same way that the single-system schemes are. Figure 11 illustrates the monthly convergence time and RMS of single-system and dual-system combination static PPP solutions, and the month median convergence time and RMS are also indicated. First, convergence time is used to assess positioning performance. For the horizontal component, the GE combination has the least convergence time of all the dual-system PPP \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Latitude** & **High\_N** & **Med\_N** & **Low\_N** & **Low\_S** & **Med\_S** & **High\_S** \\ \hline GPS\_H & 0.38 & 0.35 & 0.48 & 0.49 & 0.59 & 0.43 \\ Galileo\_H & 0.65 & 0.62 & 0.56 & 0.58 & 0.65 & 0.71 \\ BDS\_H & 0.96 & 0.90 & 1.06 & 0.94 & 1.01 & 0.97 \\ GPS\_V & 0.76 & 0.98 & 1.22 & 1.28 & 0.89 & 0.61 \\ Galileo\_V & 0.93 & 1.12 & 1.17 & 1.46 & 1.12 & 0.96 \\ BDS\_V & 2.21 & 1.55 & 1.90 & 1.79 & 1.55 & 1.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The mean RMS (unit: cm) of the different latitudes for static PPP. Figure 10: Geographical distribution of the median RMS of kinematic PPP for the selected 143 worldwide MGEX tracking stations over a month period (September 2022) using three single systems. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Latitude** & **High\_N** & **Med\_N** & **Low\_N** & **Low\_S** & **Med\_S** & **High\_S** \\ \hline GPS\_H & 2.06 & 2.36 & 3.16 & 2.29 & 2.42 & 2.90 \\ Galileo\_H & 3.32 & 6.18 & 6.49 & 4.72 & 5.76 & 4.23 \\ BDS\_H & 4.21 & 6.26 & 5.18 & 4.90 & 5.48 & 4.26 \\ GPS\_V & 3.54 & 3.53 & 5.10 & 4.27 & 3.95 & 4.29 \\ Galileo\_V & 4.63 & 8.49 & 12.70 & 7.97 & 7.99 & 5.84 \\ BDS\_V & 6.91 & 7.50 & 9.60 & 8.13 & 8.14 & 7.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The mean RMS (unit: cm) of the different latitudes for kinematic PPP. solutions, about 8.1 min. The performance of the GC combination is not as good as the GE combination. Specifically, the median convergence time of the GC combination is 9.4 min. The performance of the CE combination is not as good as the GE and GC combinations. Specifically, the median convergence time of the CE combination is 11.8 min. All three dual-system combinations have a shorter convergence time than all three single systems in the horizontal component. Similar to the horizontal component, the GE combination has the shortest convergence time in the vertical component, which is 9.0 min. The convergence time for this GC combination is about 9.5 min. The convergence time of the CE combination is 12.0 min. Both the GC and GE combination outperform GPS-only. As shown in the figure, the RMS of PPP solutions in the vertical component is vastly better than in the horizontal component. The performance of dual-system combinations is compared. The median RMS for the GC combination is 0.48 and 1.23 cm in the horizontal and vertical components, respectively; it is 0.41 and 0.99 cm for the GE combination, respectively, and it is 0.51 and 1.21 cm for the EC combination, respectively. We can see that the RMS statistics of GPS-only perform better than all three dual-system schemes. The situation with kinematic PPP is shown in Figure 12. The advantages of system combination are more obvious in kinematic PPP. The convergence time of all dual-system combination PPP solutions in the vertical component is shorter than in the horizontal component. For the horizontal component, the GE combination has the least convergence time of all dual-system PPP solutions, about 12.1 min. The median convergence time of the GC combination is 13.2 min. The performance of the CE combination is not as good as the GE and GC combinations. Specifically, the median convergence time of the EC combination is 16.2 min. All three dual systems have a shorter convergence time than GPS-only in the horizontal component. Both the GE and GC combinations have the same median convergence time in the vertical component, which is 11.5 min.