# Assessment of Affordable Real-Time PPP Solutions for Transportation Applications
## 3 Results  
To analyze the accuracy of our proposed multi-GNSS RT-PPP solutions for transportation applications, different processing scenarios were applied: GPS (G), GPS/GLONASS (GR), GPS/Galileo (GE), and GPS/GLONASS/Galileo (GRE). Furthermore, three instantaneous SSR corrections were applied, including BKG, WHU, and CNE products. The real-time SSR products were used to correct the satellite orbit and clock values. Furthermore, multi-GNSS RTK solutions were explored for transportation applications, which also included G, GR, GE, and GRE; consequently, the accuracy of around 16 solutions is under investigation in our study, as indicated in Table 2. The derived UTM coordinates from all solutions were validated against the kinematic differential solution. For vehicular transportation applications, horizontal positioning accuracy is more important than vertical accuracy; thus, 2D positioning accuracy is primarily explored in our work. Figure 6 illustrates the horizontal positioning errors for the RT-PPP solutions using different SSR corrections and RTK solutions; the RT-PPP models converge to a few decimeters, while the RTK models converge to less than one decimeter. For the RT-BKG processing scenarios, the RT-BKG-GE converges faster than the other solutions, reaching \begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**Processing Strategy**} \\ \cline{2-3}  & **RT-PPP** & **RTK** & **Differential** \\ \hline System & GPS, GLONASS, Galileo & \\ \hline Frequency & GPS: L\({}_{1}\)/L\({}_{2}\); GLONASS: G\({}_{1}\)/G\({}_{2}\); Galileo: E\({}_{1}\)/E\({}_{5b}\) \\ \hline Mathematical model & Undifferenced & Differenced & Differenced \\ \hline Observation interval & \multicolumn{2}{c}{1 HZ} \\ \hline Elevation angle & \multicolumn{2}{c}{10 degrees} \\ \hline Orbits and clocks & BKG, CNE, WHU & BRDM & IGS-Final \\ \hline Tropospheric modeling & \multicolumn{2}{c}{Saastamoinen model + VMF} \\ \hline Parameter estimation & \multicolumn{2}{c}{Kalman filter} \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of data processing strategy. Figure 5: Flow diagram for our proposed processing scenarios. less than 0.1 m; on the other hand, the other three solutions converge to 0.2 m. It can also be seen that the RT-BKG-G has a slightly longer convergence time. Likewise, compared to the other RT-CNE scenarios, the RT-CNE-GE technique has a faster convergence time. In addition, there are some variations in the 2D positioning error values for the RT-CNE-G model; there is also an obvious increment in the positioning errors for the three models at the end of the observation window, particularly the RT-CNE-GR model. To the contrary, the RT-WHU-GR solution's performance improves along with the RT-WHU-GE technique, which also demonstrates rapid convergence. Moreover, the RT-WHU-G technique has a longer convergence, approaching 0.2 m. Thus, the RTK solutions \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**GNSS**} & \multicolumn{3}{c}{**RT-PPP**} & \multirow{2}{*}{**RTK**} \\ \cline{2-3} \cline{5-5}  & **BKG** & **CNE** & **WHU** \\ \hline G & RT-BKG-G & RT-CNE-G & RT-WHU-G & RTK-G \\ \hline GR & RT-BKG-GR & RT-CNE-GR & RT-WHU-GR & RTK-GR \\ \hline GE & RT-BKG-GE & RT-CNE-GE & RT-WHU-GE & RTK-GE \\ \hline GRE & RT-BKG-GRE & RT-CNE-GRE & RT-WHU-GRE & RTK-GRE \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proposed processing solutions and their symbols. Figure 6: Two-dimensional positioning errors for the RT-PPP and RTK scenarios. are clearly superior because the positioning errors dramatically decrease to less than 0.02 m, with some fluctuations reaching 0.04 m.  
To visualize the positioning performance of the proposed RT-PPP and RTK scenarios, the cumulative distribution function (CDF) of the two-dimensional position discrepancies for each scenario is plotted (Figure 7).