# Analysis of the Impact of Multipath on Galileo System Measurements
## 4 Multipath Analysis
### Positioning Time-Series Analyses  
The last part of the experiment involved an analysis of the position time series for the relative positioning for the WUT1-WUT2 baseline obtained from the Galileo and GPS observations. Due to significant differences in the number of observed satellites for both systems, a 2-h period of the day was chosen so that both the number of visible satellites and Dilution of Precision (DOP) parameter for both systems were similar. Thus, the positions between 12 and 14 UTC were analyzed. The Position DOP values for the satellites of the respective systems assumed similar values of approximately 2.5. Figure 14b shows the visibility of the satellites of both systems along with their two-hour observation arcs with the position of the satellite in the middle epoch of the session (i.e., 13:00 UTC time). The geometry-based double-differenced ionosphere- and troposphere-fixed model, which assumes that both delays are negligible for such a short baseline, was derived in an instantaneous mode with an interval of 1 second and elevation mask of 5\({}^{\circ}\). In the GPS positioning model, the L5Q observations were not included due to their small number, whereas for Galileo, the E5 aQ observation was excluded due to its direct dependence on the E5Q observation used. For both systems, an elevation-dependent weight function was used in the stochastic model. Integer carrier-phase ambiguity resolution (AR) was performed by applying the LAMBDA method [40], and the correctness of AR was verified by comparing the determined values with known values calculated on the basis of known coordinates of the WUT1 and WUT2 stations. A correct AR was obtained for all solutions. Table 6 summarizes the RMS for the receiver positions determined in this way in relation to the reference position. The statistics concern errors for the components in the local system: north \(n\), east \(e\), and vertical \(u\). It can be seen that the receiver's position was determined with a similar accuracy. Only the elevation was found to be noticeably more accurate compared to Galileo due to the use of GPS observations. This difference may be due to the fact that, despite attempts to select the most favorable satellite visibility conditions for Galileo, it did not provide the same satellite availability as GPS. The main purpose of this comparison, however, was to try to identify, in the determined coordinate series, disturbances due to the multipath effect. For that purpose, the coordinate series were subjected to time-frequency analysis using a wavelet transform, similarly to that observed earlier. Due to the largest errors in vertical component determination, this paper presents the results only for the analysis of this particular coordinate. Figure 14a presents the time series of the receiver height. For better legibility, the graphs for both systems were placed apart. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**0-3 mHz**} & \multicolumn{2}{c}{**3-20 mHz**} & \multicolumn{2}{c}{**0–20 mHz**} \\ \cline{2-7}  & **E18** & **G9** & **E18** & **G9** & **E18** & **G9** \\ \hline
**max [m]** & 0.197 & 0.320 & 0.426 & 0.633 & 0.462 & 0.621 \\ \hline
**min [m]** & \(-0.202\) & \(-0.352\) & \(-0.586\) & \(-0.574\) & \(-0.632\) & \(-0.813\) \\ \hline
**range [m]** & 0.399 & 0.672 & 1.012 & 1.207 & 1.094 & 1.434 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum code multipath errors determined from decomposition of signal for specified satellites. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**0–3 mHz**} & \multicolumn{2}{c}{**3–20 mHz**} & \multicolumn{2}{c}{**0–20 mHz**} \\ \cline{2-7}  & **E18** & **G9** & **E18** & **G9** & **E18** & **G9** \\ \hline
**max [mm]** & 6.7 & 7.7 & 9.1 & 9.3 & 12.3 & 10.1 \\ \hline
**min [mm]** & \(-2.3\) & \(-1.4\) & \(-3.0\) & \(-3.8\) & \(-7.3\) & \(-3.5\) \\ \hline
**range [mm]** & 9.0 & 9.1 & 12.1 & 13.1 & 19.6 & 13.6 \\ \hline \hline \end{tabular}
\end{table}