## 3 Results
### Accuracy Analysis of Real-Time PPP-Estimated ZTD  
It can be seen from the previous section that the overall positioning accuracy of real-time multi-GNSS PPP was more stable, and the convergence speed was faster. Therefore, real-time PPP inversion ZTD used multi-GNSS for subsequent research. The real-time ZTD (PPP-ZTD) solved by CNES products was compared with the ZTD product released by IGS (IGS-ZTD) to evaluate its accuracy. IGS-ZTD is a postprocessing product generated by the IGS final orbit with a time resolution of 5 min and an accuracy of 5 mm as a reference [31]. The difference between the two groups of ZTD demonstrates the accuracy of PPP-ZTD. The HKSL and HKWS stations in Hong Kong are on the list of IGS continuous observation and tracking stations, so these two stations are selected for testing. Figure 4 shows the test results of the PPP-ZTD and IGS-ZTD time series and their differences between HKSL and HKWS stations during June 2021 (DOY 173-DOY 179, during rainfall periods) and August 2021 (DOY 229-DOY 235, during nonrainfall periods). The statistical results of the time series listed in Figure 4 are shown in Table 5. The RMS accuracy of PPP-ZTD at both stations during rainfall and nonrainfall periods was about 10 mm. This accuracy meets the 15 mm threshold required for the ZTD input accuracy of the NWP model used in meteorological applications [32]. The ZTD calculated from ECMWF by the integration method at GPS stations was compared with GPS ZTD. The bias ranged from 11.5 to \(-\)28.6 mm with a corresponding average of \(-\)10.5 mm, while the largest RMS was 35.4 mm with an average of 24.3 mm [33]. It can be seen that the ZTD of NWP inversion had higher accuracy. Therefore, the ZTD reference values of other stations were considered to be replaced by NWP ZTD. It can be seen from Table 6 that the accuracy of real-time PPP-ZTD during nonrainfall periods was generally higher than that during rainfall periods. During nonrainfall periods, the RMS of real-time PPP-ZTD was about 10 mm, except for individual stations. The RMS of real-time PPP-ZTD was generally around 15 mm during rainfall. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Station**} & **E** & **N** & **U** & **Convergence** & **E** & **N** & **U** & **Convergence** \\  & **(cm)** & **(cm)** & **Time (min)** & **(cm)** & **(cm)** & **(cm)** & **(cm)** & **Time (min)** \\ \cline{2-8}  & \multicolumn{4}{c}{**During Rainfall**} & \multicolumn{4}{c}{**During Nonrainfall**} \\ \hline HKSL & 1.77 & 0.83 & 2.59 & 38 & 1.35 & 0.86 & 1.71 & 34 \\ HKWS & 1.19 & 0.57 & 2.13 & 50.5 & 1.06 & 0.87 & 1.43 & 28 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Positioning error and convergence time of real-time multi-GNSS PPP. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Station**} & **Bias (mm)** & \begin{tabular}{c} **STDEV** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **RMS** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Bias (mm)** \\ **(mm)** \\ \end{tabular} & \
\begin{tabular}{c} **STDEV** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **RMS** \\ **(mm)** \\ \end{tabular} \\ \cline{2-6}  & \multicolumn{4}{c}{**During Rainfall**} & \multicolumn{4}{c}{**During Nonrainfall**} \\ \hline HKSL & 5.43 & 9.14 & 10.52 & 2.1 & 9.72 & 9.91 \\ HKWS & 4.08 & 8.91 & 9.88 & 2.42 & 8.85 & 9.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Bias, STDEV, and RMS between PPP-ZTD and IGS-ZTD.