# A New Zenith Tropospheric Delay Grid Product for Real-Time PPP Applications over China
## 4 Real-Time ZTD Grid Product Evaluations
### PPP Convergence Tests  
RtZTD can provide users with high-accuracy _a priori_ ZTD, which can be used to accelerate the PPP convergence. 95 stations with both GPS and BDS observations available from National BDS Augmentation Service System (NBASS) are selected as test stations in PPP convergence tests. All CMONOC stations were used as base stations to generate RtZTD product with a resolution of 0.75\({}^{\circ}\)\(\times\) 0.75\({}^{\circ}\) in the simulated real-time mode. The tests cover one week from 4 Apr to 10 Apr 2016 and the GPS/BDS data were processed with 30 s interval. The convergence time of PPP using RtZTD product (denoted as RtZTD) and the traditional PPP (Saastamoinen + GPT2w as _a priori_, and the remaining part is estimated) (denoted as non-RtZTD) will be compared.  
For each test station, we calculated the differences between coordinates derived from PPP and the ground-truth (estimated in post-processing mode) in horizontal and vertical components, respectively. Afterwards, at each epoch, the coordinate absolute differences were sorted from lowest to highest. The maximum value among 95% (2\(\sigma\)) or 68% (1\(\sigma\)) of the sorted coordinate differences at each epoch is selected [35] and plotted in Figure 8. As shown in Figure 8, in both 95% and 68% situations, using RtZTD can significantly accelerate the convergence. After 60 and 30 min for BDS- and GPS-PPP, for example, coordinate errors decrease from 0.57 to 0.39 m in horizontal component and from 0.72 to 0.37 m in vertical component for BDS-PPP using RtZTD in 95% situation. For GPS-PPP, the errors decrease from 0.60 to 0.52 m and from 0.35 to 0.24 m in horizontal and vertical components, respectively.  
Figure 7: Comparison of GPT, GPT2, EGNOS, UNB3m model and RTZTD (stations sorted in ascending altitude).  
According to the statistics of coordinate error RMS after convergence (the first-three-hour results removed) as shown in Table 6, we set the thresholds for convergence as 0.4 and 0.2 m of coordinate errors for BDS- and GPS-PPP, respectively, in 95% situation, while the thresholds as 0.2 and 0.1 m for BDS and GPS, respectively, in 68% situation.  
Table 7 summarizes the PPP convergence time of non-RtZTD and RtZTD cases. For BDS-PPP, the convergence time improved about 32% and 65% in the horizontal and vertical components in 95% situation, respectively, and improved up to 6% and 65% in 68% situation. For GPS-PPP, although there are no significant improvements in the horizontal component, the improvements in the vertical direction are approximately 29% and 25% in 95% and 68% situation, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Non-RtZTD PPP**} & \multicolumn{4}{c}{**RtZTD PPP**} \\ \cline{2-9}  & **H (95\%)** & **H (68\%)** & **V (95\%)** & **V (68\%)** & **H (95\%)** & **H (68\%)** & **V (95\%)** & **V (68\%)** \\ \hline BDS & 13.91 & 4.36 & 22.26 & 8.78 & 13.60 & 4.53 & 19.28 & 7.70 \\ GPS & 9.41 & 2.30 & 10.81 & 3.47 & 9.34 & 2.47 & 11.92 & 4.86 \\ \hline \hline \end{tabular}
\end{table}
Table 6: RMS of the positioning error after convergence (the first-three-hour results removed) (unit: cm).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Non-RtZTD PPP**} & \multicolumn{4}{c}{**RtZTD PPP**} \\ \cline{2-9}  & **H (95\%)** & **H (68\%)** & **V (95\%)** & **V (68\%)** & **H (95\%)** & **H (68\%)** & **V (95\%)** & **V (68\%)** \\ \hline BDS & 84.5 & 62 & 149.5 & 87.5 & 57.5 & 58 & 52 & 30.5 \\ GPS & 73.5 & 60.5 & 62.5 & 36 & 71.5 & 57.5 & 44.5 & 27 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Convergence time comparisons of non-RtZTD and RtZTD PPP (unit: min) \({}^{*}\).  
Figure 8: Convergence time comparison for BDS/GPS PPP in horizontal component and vertical component.