## 2 Data and Methodologies
### ZTD and PWV Estimation with PPP
For BDS-3, the daily mean STD values of the clock errors vary from 0.06 ns to 0.29 ns, with 96.3% and 68.9% of the values being smaller than 0.2 ns and 0.15 ns, respectively. For the orbit corrections, the latencies were in the range of 21-30 s, which is within the nominal validity of the satellite orbit corrections, that is, 96 s. As shown in Table 2, both GPS and BDS-3 have a higher accuracy in the radial direction than in the along- and cross-track directions. The mean RMSEs for the GPS satellites were 0.08 m, 0.36 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively. For the BDS-3 MEO satellites, the mean RMSEs were 0.10 m, 0.27 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively, which were similar to those of the GPS satellites. For the BDS-3 IGSO satellites, the mean RMSEs in the radial, along-track, and cross-track directions were 0.13 m, 0.37 m, and 0.40 m, respectively, which were worse than those of the BDS-3 MEO and GPS satellites. The results reveal obvious day-to-day variations in the orbit errors for both GPS and BDS-3, especially in the along- and cross-track directions. For GPS, the daily mean RMSEs of the 3D orbit errors vary from 0.22 m to 0.85 m, 57.5% of which are smaller than 0.5 m. For BDS-3, the daily mean RMSEs of the 3D orbit errors vary from 0.19 m to 0.96 m, 71.5% of which are smaller than 0.5 m. The accuracy of ZTD estimation in PPP is heavily dependent on the precision of orbit and clock corrections. [PERSON] [78] reports that tangential orbit errors of 10 cm or radial orbit errors of 1 cm can induce ZTD errors of up to 1.3 cm and 1.0 cm, respectively. However, their study also demonstrated that precise satellite clock corrections can mitigate over 96% of radial orbit errors, aided by the small nadir angle (15\({}^{\circ}\)) and ambiguity resolution in PPP. Consequently, even with decimetre-level orbit errors, centimetre-level accuracy for ZTD, and millimetre-level accuracy for PWV, assuming a scale factor of 0.15 between the ZTD and PWV [5], can be achieved, as most \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**System**} & \multirow{2}{*}{
\begin{tabular}{c} **STD of Clock Errors** \\ **(ns)** \\ \end{tabular} } & \multicolumn{3}{c}{**RMSE of Orbit Errors (m)**} \\ \cline{2-4}  & & **Radial** & **Along-Track** & **Cross-Track** \\ \hline GPS & 0.16 & 0.08 & 0.36 & 0.28 \\ BDS-3 MEO & 0.13 & 0.10 & 0.27 & 0.28 \\ BDS-3 IGSO & 0.18 & 0.13 & 0.37 & 0.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation of the PPP-B2b orbit and clock. orbit errors can be compensated by precise satellite clock corrections and the estimated ambiguity parameter in the PPP approach. The DCBs that refer to the B3I signal at frequencies of \(f_{\rm B1I}\), \(f_{\rm BIC}\), and \(f_{\rm B2a}\) for BDS-3 were compared to those from DLR and CAS provided by the MGEX pilot project, and the mean values of the differences for the study period are shown in Table 3. The systematic bias between each DCB product caused by the zero-assumption adopted in the DCB estimation must be removed before the comparison is conducted. This systematic bias between different DCB products is absorbed by the receiver clock parameter and, thus, does not affect the final positioning or ZTD results. Table 3 shows the STD values of the differences between the different DCB products. We found that the STDs of the differences between the DCBs of DLR and CAS are 0.15 ns, 0.14 ns, and 0.13 ns for frequencies of \(f_{\rm B1I}\), \(f_{\rm BIC}\), and \(f_{\rm B2a}\), respectively. For the frequencies \(f_{\rm BIC}\), \(f_{\rm B2a}\), and \(f_{\rm B1I}\), the STD values of the differences between the DCB from PPP-B2b and the DCB from DLR or CAS were all within 0.4 ns. Although the error in the DCB would lead to a longer convergence time, it could be mostly absorbed by the receiver clock and ambiguity parameter for PPP and, thus, had no effect on the accuracy of the troposphere and coordinate estimates.