# Analysis of the Impact of Multipath on Galileo System Measurements
## 4 Multipath Analysis
### Phase Multipath Analysis  
The multipath effect for phase observations was determined based on the methodology presented in Section 3.2, using measurements from the very-short baseline WUT1-WUT2. When creating DD combinations, the reference satellite was the satellite with the highest \begin{table}
\begin{tabular}{r c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Galileo**} & \multicolumn{4}{c}{**GPS**} \\ \cline{2-10}  & **E1C** & **E5 aQ** & **E5 bQ** & **E5Q** & **E6C** & **L1C/A** & **L2C(L)** & **L2W** & **L5Q** \\ \hline \hline
**el [\({}^{\circ}\)]** & & & & & & \(\sigma\,M\) **[m]** & & & \\ \hline
**15** & 0.192 & 0.181 & 0.192 & 0.130 & 0.196 & 0.223 & 0.236 & 0.402 & 0.197 \\ \hline
**30** & 0.137 & 0.122 & 0.140 & 0.090 & 0.136 & 0.153 & 0.160 & 0.285 & 0.137 \\ \hline
**80** & 0.041 & 0.051 & 0.054 & 0.031 & 0.045 & 0.047 & 0.060 & 0.117 & 0.062 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Standard deviation of the code multipath error for a specified elevation estimated on the basis of the model. Figure 5: Three-dimensional distribution of a code multipath error at the WUT2 site for **(a)** E1C Galileo and **(b)** L1 C/A GPS observations. elevation at a given epoch. The elevation of this satellite for most epochs was above 60\({}^{\circ}\). For such elevations, the measurement noise is stabilized and its changes over time are minimized. The analysis of the code multipath shows that, additionally, the magnitude of the multipath impact for high satellites stabilizes. Therefore, it may be assumed that the impact of both noise and the multipath effect for reference satellites has constant values and that any changes of these parameters may be interpreted in relation to observations of non-reference satellites. Thus, the presented analyses of satellite elevation are related to changes in the elevation of non-reference satellites. It can be assumed that the multipath impact on carrier-phase observations does not depend on the type of modulation but solely on the carrier wavelength (the longer the wavelength, the greater the multipath error) [2]. The results obtained in the experiment confirm this assumption for all observations, regardless of the system, but only for the lowest elevations (see Figure 6). The lowest STD values for satellites at elevations up to 20\({}^{\circ}\) were thus obtained for observations at L1/E1 frequencies for both systems. For higher elevations, the relation between the multipath error and the carrier wavelength disappears. What is important for phase multipath is that no differences were recorded between the observations for the two systems other than due to differences in the carrier wavelengths of given signals. Disproportionately higher values of the multipath for the L5 GPS signal may result from the fact that this signal is measured from the smallest number of satellites. In addition, the reference satellites for this observation had the lowest elevations. With increasing satellite elevation, the value of measurement noise decreases, and for elevations above 40\({}^{\circ}\), it stabilizes at a constant level of approximately 0.5 mm (see Figure 7). It is clearly visible that higher noise values have been obtained for the E5a and E6 Galileo as well as L2C and L2W GPS observations. Figure 6: Standard deviation of phase multipath error versus elevation. Figure 7: Standard deviation of phase noise error versus elevation. Just as in the case of code multipath, a model of the correlation between the standard deviation and the satellite elevation was created (see Figure 8). For this purpose, a third-degree polynomial was selected again. The obtained values of the R-squared coefficients, listed in Figure 8, allow for the consideration of the model fit to the data to be sufficient. Model values of STD for three satellite elevations are presented in Table 3. Similarly to Figure 8, the correlation between the multipath impact and the carrier wavelength is visible only for the lowest satellite elevation.