## 4 Conclusions  
In this work, the performances of static multi-GNSS PPP are analyzed; several configurations are considered. The used GNSS are GPS, GLONASS, and Galileo and all their possible combinations are assessed. Two different tropospheric models are tested: Saastamoinen and Estimate ZTD. The benefit of using precise clock products at 30 s, instead of classic products at 15 min, is evaluated.  
In order to carry out a significant analysis, a large amount of data is processed  
* A dataset of GNSS measurements, stored at a permanent station, acquiring 24 h a day for 1 month (Test A)
* A dataset of GNSS measurements, stored by a geodetic receiver on a pillar, acquiring about 6 h a day for 10 days (Test B)  
The open-source software RTKLib is used for the processing. Daily solutions are obtained by RTKLib, their standard deviation is considered to assess the stability of the processing, while the mean of the daily solutions is the final solution. The known position of the used receivers is the reference for the error analysis.  
Final solutions and standard deviations of the daily solutions are used to implement an outlier rejection strategy in the position domain due to the inefficiency of the applied RAIM-FDE algorithm to detect and exclude the outlier from the measurements set.  
From the comparison between the tropospheric models Saastamoinen and Estimate ZTD, it is clear that the second allows for better performance. About the GNSS combinations, GPS-only and GLONASS-only cases provided similar performance, while the Galileo-only performances are slightly degraded. The use of double constellations is generally beneficial, and particularly promising results are obtained with the GPS+Galileo combination. The triple combination GPS+GLONASS+Galileo provides the best performance for both tests; in particular, errors of a few millimeters are obtained in Test A, and one order of magnitude larger for Test B, probably because the last is significantly shorter  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**GNSS Combination**} & \multicolumn{2}{c}{**Standard Deviation (mm)**} & \multicolumn{3}{c}{**Error (mm)**} \\ \cline{2-7}  & \(\sigma_{\mathbf{x}}\) & \(\sigma_{\mathbf{y}}\) & \(\sigma_{\mathbf{z}}\) & \(\mathbf{x}\) & \(\mathbf{y}\) & \(\mathbf{z}\) \\ \hline GPS & 77 & 144 & 23 & \(-\)53 & \(-\)171 & \(-\)27 \\ GLONASS & 26 & 83 & 16 & \(-\)9 & 91 & 20 \\ Galileo & 744 & 568 & 466 & 218 & 188 & 27 \\ GPS+GLONASS & 40 & 57 & 13 & \(-\)55 & \(-\)31 & \(-\)4 \\ GPS+Galileo & 63 & 109 & 13 & \(-\)47 & \(-\)149 & \(-\)24 \\ GLONASS+Galileo & 74 & 66 & 79 & \(-\)4 & 75 & 9 \\ GPS+GLONASS+Galileo & 31 & 50 & 9 & \(-\)49 & \(-\)1 & \(-\)1 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Standard deviations and errors of the considered GNSS combinations with Estimate ZTD tropospheric models (outlier rejections).  
The use of precise clock products at 30 s demonstrates to increase significantly the PPP performance; indeed, in GPS-only case the tridimensional error from 2.5 cm (with the clock data at 15 min) to 1.3 cm (with the clock data at 30 s).  
Conceptualization, A.P., C.P., and G.D.; Writing--original draft, A.P., C.P., and G.D.; Writing--review and editing, A.A., A.I. and S.G.; Methodology, G.D., A.A.; Software and formal analysis, A.P., C.P., and G.D.; Data curation and visualization, A.A., A.I. and S.G.; Supervision, G.D., A.A. and S.G.; Validation A.A., A.I. and S.G. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.