# Precise Point Positioning Using Triple GNSS Constellations in Various Modes
## 5 Results and Discussion  
To verify the developed combined PPP model, three-constellation GNSS (GPS, Galileo, and BeiDou) observations at four globally distributed stations were selected from the IGS tracking network (Figure 1) [36]. Those stations are occupied by GNSS receivers, which are capable of simultaneously tracking the GNSS constellations. Only one hour of observations with maximum possible number of Galileo and BeiDou satellites at each station is considered in our analysis. All data sets have an interval of 30 s.  
The positioning results for station Delf1 located at Delft University of Technology, The Netherlands, are presented below. Similar results are obtained for the other stations. However, a summary of the convergence times and the three-dimensional PPP solution standard deviations are presented below for all stations. Natural Resources Canada's GPSpace PPP software is modified to handle data from GPS, Galileo, and BeiDou systems, which enables a combined PPP solution as detailed above. BNC version 2.11.1 software is used to combine GPS and Galileo observations to obtain a real-time PPP solution. In addition to the combined PPP solution, we also obtained the PPP solutions of the un-differenced ionosphere-free GPS-only, which is used to assess the performance of the newly developed PPP model. Figure 2 summarizes the satellite availability during the one-hour observation time for each constellation at DLF1 station. As shown in Figure 2, eight to nine GPS satellites were visible during the one-hour observation time span. The addition of Galileo and BeiDou systems increase the number of visible satellites to 19-20. \begin{table}
\begin{tabular}{c c c} \hline
**Product** & **Format** & **Frequency** \\ \hline GNSS Data & RTCM 3 & 1 s \\ GPS orbit corrections & RTCM-SSR & 5 or 60 s \\ GPS clock Corrections & RTCM-SSR & 5 s \\ \hline \end{tabular}
\end{table} 
Table 1: Outlines the IGS RTS products, their formats and frequency. Figure 3 summarizes the convergence times for all un-differenced post-processing PPP models with different GNSS constellation combinations. As can be seen, the un-differenced GPS-only post-processed PPP solution indicates that the model is capable of obtaining a sub-decimetre level accuracy. However, the solution takes about 20 min to converge to decimetre level precision. As shown in Figure 3, the convergence time of the combined GNSS post-processed PPP solutions takes about 15 min to reach the decimeter level precision, which represent a 25% improvement in comparison with the GPS-only post-processed PPP solution. To further assess the performance of the various un-differenced post-processing PPP models, the solution output is sampled every 10 min and the standard deviation of the computed station coordinates is calculated for each sample. Figure 4 shows the position standard deviations in the East, North, and Up directions, respectively. As can be seen, the precision of the combined un-differenced post-processed PPP solutions is comparable to that of the GPS-only post-processed PPP solution. Figure 1: Analysis stations. Figure 2: DLF1 station GNSS satellite availability. Figure 5 summarizes the convergence times for the GNSS BSSD post-processed PPP solutions using different reference satellites. As shown in Figure 5, using BSSD post-processing PPP model reduces the convergence time to 10 min, which represents a 50% improvement compared to the GPS-only post-processed PPP solution. Similar to the un-differenced solution, the BSSD solution output is sampled every 10 min and the standard deviation of the estimated station coordinates is calculated for each sample. Figure 4: Summary of positioning standard deviations in East, North, and Up directions of all un-differenced post-processed PPP solutions. (**a**) East standard deviation; (**b**) North standard deviation; (**c**) Up standard deviation. Figure 3: Summary of convergence times for post-processing PPP solutions at all stations.