## 4 PPP-B2b ZTD Estimation and Evaluation of the Results  
### Evaluation of Real-Time PPP-B2b ZTD at Station BJ01  
Using the PPP-B2b corrections and GNSS observations received in real time at station BJ01, the real-time ZTD was computed and compared to the post-processed ZTD, which was calculated using a combination of GPS and BDS-3 constellations with accurate orbit and clock products from GBM from DOY 117 to the end of DOY 130, 2022. As shown in Figure 4a, the ZTDs derived using the PPP-B2b method with different systems agreed very well with those derived from GBM products. The results in Figure 4b depict that while the differences between PPP-B2b ZTD and GBM ZTD generally fall within the range of \(\pm 3\) cm, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**System** & **Satellite Type** & \begin{tabular}{c} \(SISRE_{orb}\) \\ **[RMSE]** \\ \end{tabular} & \
\begin{tabular}{c} \(SISRE_{clk+orb}\) \\ **[RMSE]** \\ \end{tabular} &
\begin{tabular}{c} \(SISRE_{clk+orb}\) \\ **[STD]** \\ \end{tabular} \\ \hline \multirow{4}{*}{GPS} & IIR & 0.11 & 1.94 & 0.07 \\  & IIR-M & 0.10 & 0.94 & 0.06 \\  & IIF & 0.11 & 0.96 & 0.06 \\  & III & 0.12 & 0.63 & 0.04 \\  & Mean & 0.11 & 1.12 & 0.06 \\ \hline \multirow{4}{*}{BDS-3} & MEO & 0.12 & 0.58 & 0.03 \\  & IGSO & 0.14 & 0.87 & 0.04 \\ \cline{1-1}  & Mean & 0.13 & 0.72 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical results for the SISREs (unit: m). Figure 3: Daily variation in \(SISRE_{clk+orb}\) [STD] for (**a**) GPS and (**b**) BDS-3 from DOY 069 to 311 in 2022. The results show that the daily \(SISRE_{clk+orb}\) remains less than 0.1 m for GPS and less than 0.05 m for BDS-3 most of the time. there is noticeable daily variation in these differences. This variation could be attributed to the daily fluctuations in the accuracy of the PPP-B2b orbit/clock products. As listed in Table 5, using the post-processed ZTDs derived with the GBM final orbit/clock products as a reference, the ZTD errors stemming from the PPP-B2b corrections were calculated across different satellite systems. Table 5 shows that the ZTDs derived from GPS observations have the smallest bias but the largest RMSE compared to those of the other solutions. The ZTDs derived from the BDS-3 observations have an RMSE of 13.9 mm, which is slightly larger than that of the ZTDs derived from the combination of BDS-3 and GPS observations but smaller than that of the GPS-only solution. As shown in Table 5 and Figure 5, 91% of the errors for the GPS-only solution were in the range of \(-\)30 mm to 30 mm, while the percentage for the other solutions reached approximately 98%. For the coordinate accuracy, the RMSEs were 0.9 cm, 0.6 cm, and 4.8 cm in the north, east, and vertical directions, respectively, for the BDS-3/GPS combination solution, which is slightly better than the GPS-only or BDS3-only solution. As suggested by [PERSON] et al. [80], a scaling factor of 4.4 between ZTD and station height is observed for a 10\({}^{\circ}\) elevation cutoff angle, meaning that a 4.4 cm error in station height corresponds to a 1 cm error in ZTD. Thus, theoretically, a 4.8 cm error in station height would result in approximately a 1 cm error in the ZTD estimate, which would result in about a 2 mm error in the derived PWV, assuming a scaling factor of 0.15 between ZTD and PWV [5]. Figure 4: ZTD time series derived with different methods (**a**) and the differences between ZTDs derived with PPP-B2b and GBM (**b**). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Strategy** & **Error Range** & **Percentage in the Range** & **Bias (mm)** & **RMSE (mm)** \\  & **[Min, Max]** & **[\(-\)30 mm, 30 mm) (\%)** & **Bias (mm)** & **RMSE (mm)** \\ \hline GPS-only & [\(-\)57.7, 67.5] & 91.1 & \(-\)0.3 & 17.8 \\ BDS-only & [\(-\)41.9, 32.2] & 98.5 & \(-\)6.4 & 13.9 \\ BDS + GPS & [\(-\)44.6, 40.3] & 98.2 & \(-\)2.5 & 13.4 \\ \hline \hline \end{tabular}
\end{table}