## 3 Results and Discussion
### Preliminary Analyses (Test A)
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Saastamoinen**} & \multicolumn{3}{c}{**Estimate ZTD**} \\ \cline{2-7}
**GNSS Combination** & \multicolumn{3}{c}{**Standard Deviation (mm)**} & \multicolumn{3}{c}{**Standard Deviation (mm)**} \\ \cline{2-7}  & \(\mathbf{\sigma_{\mathrm{x}}}\) & \(\mathbf{\sigma_{\mathrm{y}}}\) & \(\mathbf{\sigma_{\mathrm{z}}}\) & \(\mathbf{\sigma_{\mathrm{x}}}\) & \(\mathbf{\sigma_{\mathrm{y}}}\) & \(\mathbf{\sigma_{\mathrm{z}}}\) \\ \hline GPS & 409 & 93 & 104 & 510 & 313 & 332 \\ GLONASS & 87 & 47 & 60 & 57 & 48 & 25 \\ Galileo & 101 & 69 & 67 & 292 & 54 & 462 \\ GPS+GLONASS & 125 & 17 & 73 & 84 & 17 & 54 \\ GPS+Galileo & 264 & 154 & 142 & 281 & 54 & 141 \\ GLONASS+Galileo & 77 & 35 & 59 & 54 & 42 & 36 \\ GPS+GLONASS+Galileo & 117 & 27 & 68 & 175 & 39 & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Standard deviation of the considered GNSS combinations with Saastamoinen and Estimate ZTD (Zenith Tropospheric Delay) tropospheric models. Figure 8: Daily estimations of X component with Saastamoinen and Estimate ZTD (Zenith Tropospheric Delay) tropospheric models in case of GPS-only configuration (**a**) no outlier rejection (**b**) outlier rejection. coordinates of the daily solutions for GPS-only case, after the rejection of the anomalous daily solutions, are shown in Figure 8b. The solutions in this case are clearly more consistent and the Estimate ZTD seems to provide more stable solutions with respect to the Saastamoinen model. In Table 3, the standard deviations of the considered configurations, with the application of the previously mentioned outlier rejection strategy, are shown; in this case, the standard deviation values are significantly reduced with respect to the previous case (Table 2). Comparing the configurations with the Saastamoinen and Estimate ZTD tropospheric models, what becomes evident are the benefits of using the second one. Focusing on the configurations with Estimate ZTD model:  
* the stabilities of single GNSS combinations are similar, with slightly best performance for GLONASS-only case;
* the stabilities of double GNSS combinations are increased with respect to the single GNSS case, the best performances are obtained with GPS+Galileo constellations, and the worst performances are obtained with GLONASS+Galileo;
* the stability of the triple GNSS combination is similar to double constellations cases. In Table 4, the position errors obtained with the considered configurations, applying the outlier rejection strategy, are shown. Even analyzing the position errors, it is evident the benefit of using Estimate ZTD with respect to the Saastamoinen model. Focusing only on configurations with the Estimate ZTD model, the GPS-only and GLONASS-only performances are very similar, while larger errors are evident for the Galileo-only case. The use of double constellations is surely advantageous and, in particular, a sub-cm level positioning is obtained with the GPS+Galileo combination. The better stability of GPS and Galileo, with respect to GLONASS, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Saastamoinen**} & \multicolumn{3}{c}{**Estimate ZTD**} \\ \cline{2-7}
**GNSS Combination** & \multicolumn{3}{c}{**Error (mm)**} & \multicolumn{3}{c}{**Error (mm)**} \\ \cline{2-7}  & x & y & z & x & y & z \\ \hline GPS & 49 & \(-\)3 & 37 & 17 & 3 & 18 \\ GLONASS & 26 & \(-\)17 & 20 & 16 & \(-\)4 & 10 \\ Galileo & \(-\)64 & \(-\)16 & \(-\)43 & \(-\)31 & \(-\)5 & \(-\)29 \\ GPS+GLONASS & 36 & \(-\)8 & 28 & 11 & 1 & 10 \\ GPS+Galileo & \(-\)6 & 14 & 11 & \(-\)2 & 8 & \(-\)2 \\ GLONASS+Galileo & 1 & \(-\)19 & \(-\)4 & \(-\)5 & \(-\)8 & \(-\)6 \\ GPS+GLONASS+Galileo & 21 & 5 & 11 & 1 & \(-\)2 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Errors of the considered GNSS combinations with Saastamoinen and Estimate ZTD tropospheric models (outlier rejections).