## 6 Discussion  
At present, the cost-effective dual-frequency multi-GNSS modules are widely utilized in precise navigation and positioning applications; in addition, there are a number of precise multi-GNSS satellite orbit and clock products which improve the multi-GNSS RT-PPP accuracy. Examples for these products include BKG, CNE, GFZ, IGS, and WHU products; as a result, in our study, we propose an ultra-low-cost real-time multi-GNSS PPP solution employing the ZED-F9P device and the five aforementioned products. Our proposed PPP solutions are validated for positioning and tropospheric applications. To provide a reference solution, the geodetic-grade Trimble R4s receiver post-processed PPP is employed. Table 2 summarizes the statistical metrics of the 3D positioning, such as mean and RMSE, to analyze the achieved positioning accuracy. As can be seen, few-decimeter 3D positioning accuracies can be attained through the GPS PPP model using the five products; moreover, the Galileo 3D position is better than those of GLONASS and BeiDou, with an RMSE value less than 0.5 m. An exception is GFZ and WHU products. GLONASS 3D positioning errors are large because of the satellites' configuration and the products' accuracy. For the BeiDou solution, the three-dimensional errors are at the meter level, with slight improvements for WHU products. This is due that the ZED-F9P collects only BeiDou signals, as well as the available product's accuracy. For comparison between products, WHU provides more accurate GPS and BeiDou solutions than the other products, while BKG offers the accurate GLONASS and Galileo solutions. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Product**} & \multicolumn{2}{c}{**GPS-PPP**} & \multicolumn{2}{c}{**GLONASS-PPP**} & \multicolumn{2}{c}{**Galileo-PPP**} & \multicolumn{2}{c}{**BeiDou-PPP**} \\ \cline{2-9}  & **Mean** & **RMSE** & **Mean** & **RMSE** & **Mean** & **RMSE** & **Mean** & **RMSE** \\ \hline BKG & 0.168 & 0.253 & 1.031 & 1.123 & 0.318 & 0.419 & – & – \\ \hline CNE & 0.155 & 0.225 & 1.135 & 1.302 & 0.303 & 0.496 & – & – \\ \hline GFZ & 0.249 & 0.319 & 1.247 & 1.488 & 0.625 & 0.854 & 1.486 & 2.151 \\ \hline IGS & 0.248 & 0.307 & 1.167 & 1.298 & 0.279 & 0.451 & 2.235 & 2.804 \\ \hline WHU & 0.120 & 0.164 & 1.416 & 1.603 & 0.466 & 0.980 & 0.858 & 1.402 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Three-dimensional position statistics for the static PPP solutions (in meters). Figure 12: CDF for PWV errors for different PPP models. Furthermore, to explore the extracted PWV's precision, the statistical measures for the PWV differences over the three investigated days are determined. Table 3 lists the mean and STD values. It can be said that the WHU-derived GPS PWVs are more precise than those of the other products, with an STD less than 2.78 mm; in addition, IGS products offer precise PWV values, taking into account that IGS streams have some discontinuities on the three days. The STD values for the obtained GLONASS PWVs are large in comparison with the other solutions, with superiority to BKG products. For the real-time PWV obtained through Galileo solutions, both GFZ and WHU products supply precise PWVs with respect to the others, with superiority to GFZ products, and the precision of the GFZ-acquired BeiDou PWVs are better than those of IGS and WHU products, with STD value less than 9.45 mm.