# Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations
## 4 Results and Analysis  
### ZTD from Single-GNSS  
About 55 globally distributed stations from the MGEX network are processed in PPP mode with 30 s sampling interval to generate ZTD for the year 2019, where the simultaneous availability of GPS, BDS, Galileo, and GLONASS observations is required to examine the performance of the ZTD estimated from single-system and multi-GNSS combined solutions. The single-system (GPS, BDS, Galileo, GLONASS,), two-system (GPS + BDS, GPS + Galileo, GPS+GLONASS), three-system (GPS + BDS + Galileo, GPS + BDS + GLONASS, GPS + Galileo + GLONASS), and four-system (GPS + BDS + Galileo + GLONASS) solutions, are \begin{table}
\begin{tabular}{c c c c} \hline \hline
**RS Station** & **GNSS Station** & **Elevation Difference (m)** & **Distance (km)** \\ \hline
82281 & SALU & 16 & 2.1 \\
82022 & BOAV & 67 & 1.6 \\
91938 & TITG & 79 & 3.3 \\
91948 & GAMB & 58 & 0.5 \\
83971 & POAL & 47 & 10.0 \\
57494 & WUH2 & \(-\)4 & 23.8 \\
94610 & CUT0 & \(-\)7 & 9.7 \\
94975 & HOB2 & \(-\)1 & 4.3 \\
03882 & HERS & 26 & 3.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Radiosonde stations used in this study. adopted to derive ZTD. Weekly or biweekly fixes are made to a solution to correct the station coordinates. In order to know the performance of ZTD estimation with adding BDS-3 observation data, the two stations, DGAR (7.3\({}^{\circ}\)S, 72.4\({}^{\circ}\)E) at Diego Garcia Island, UK and PTGG (14.5\({}^{\circ}\)N, 121.0\({}^{\circ}\)E) at Taguig City, Philippines, with the highest number of BDS annual observation satellites were selected. The time series of ZTD at the two stations are displayed in Figure 2. In general, the GPS-, BDS-, Galileo-, and GLONASS-estimated ZTD agree well, except for some outliers in the BDS-only solution. In Figure 2, significant fluctuations can be seen around 260 days at DGAR station and around 200 days at PTGG station. We investigated the BDS observation satellites during these periods and found that only three BDS-3 MEOs satellites were observed at DGAR station, while fewer than three BDS satellites were observed at PTGG station during DOY 199-202, which undoubtedly exacerbates the uncertainty of ZTD estimation in this region. This also indicates that the incomplete establishment of BDS-3 cannot cover all time periods in Southeast Asia. Compared to other navigation systems, GPS was developed earlier and has more full constellations. The most developed ZTD research is based on GPS. In order to analyze whether the ZTD estimated by the observation data of other constellation systems has a beneficial effect, this paper used the ZTD retrieved by GPS as a standard to explore the correlation with the ZTD from three other single systems. The BDS-derived ZTD data present larger noise and more outliers. ZTD scatter graphs between the GPS-only and the other single-system (BDS, Galileo, and GLONASS) solutions are shown in Figure 3 for stations DGAR and PTGG. At DGAR, the correlation coefficients of ZTD are 0.98, 0.99, and 0.99, and at PTGG, the correlation coefficients are 0.98, 0.99, and 0.99, implying that linear correlation between the GPS and other three systems is very high. Figure 2: ZTD time series of GPS (G), BDS (C), Galileo (E), and GLONASS (R) for the year 2019 (**top panel**: DGAR; **bottom panel**: PTGG). The distribution of ZTD differences between the GPS-only and the other single-system solutions at DGAR and PTGG stations is shown in Figure 4. The ZTD differences in absolute values are mostly below 20 mm on average, and occasionally 20 to 30 mm. Between the GPS-only solution and the other single-system solutions, the root mean square (RMS) values of ZTD differences are 7.9, 5.9, and 6.3 mm for DGAR station, and 9.5, 6.4, and 6.8 mm for PTGG station, indicating good consistency within several millimeters. The mean biases of ZTD differences are \(-\)3.8, \(-\)0.2, and 1.3 mm for DGAR, and \(-\)0.4, \(-\)0.4, and 0.3 mm for PTGG.