# Analysis of the Impact of Multipath on Galileo System Measurements
## 4 Multipath Analysis
Again, the observation type that stands out is the E5 AltBOC signal, for which the obtained noise values are much smaller. Galileo observations have better measurement noise properties than GPS observations. Only in the case of the modernized L5 observation are the obtained results comparable to that of the Galileo system. Since the correlation between the multipath impact on code observations and the elevation of satellites is evident, a model was designed to describe it in the form of a polynomial of the third degree. The general equation can be formulated as follows:  
\[f(x)=a_{1}x^{3}+a_{2}x^{2}+a_{3}x+a_{4} \tag{30}\]  
where \(f(x)\) is the model value of \(STD_{M}\), \(a\) is the model parameters, and \(x\) is the value of the variable (satellite elevation). The values of STD of the multipath effect determined for smaller, five-degree elevation bins were selected as the test data for the model. Preliminary analyses pointed to the third-degree polynomial as the function best describing the relation between multipath and satellite elevation. The third-degree is a trade-off between accuracy and quality of fitting the polynomial curve to the data. Higher degree polynomials fit the data perfectly but do not represent them in an expected manner. The determined functions are presented in Figure 4 along with the values of the R-Squared determination coefficient, which indicates the quality of the model fit to the data. Values of the coefficient ranging from 0.97 to 0.99 indicate a very good fit of the model to the given values of STD. Based on the equations describing the multipath with respect to elevation, the model values for three selected satellite elevations were calculated (see Table 2). The obtained model STD values for an elevation of 15\({}^{o}\) for each of the Galileo observations are smaller than those for GPS. Only for the L5 GPS observation are the results comparable to the Galileo observations. The STD values for the L1 C/A and L2C(L) observations are similar and are 3-4 cm higher than in the case of the Galileo observations, with the exception of E5. The multipath error values for the E5 AltBOC signal are significantly smaller in each case than those for the other observation types. The STDs of the multipath for L2W observations, 40 cm, 29 cm, and 12 cm, are about twice as large as the errors for the other signal types. For satellites close to the zenith, the value of the multipath error is approximately 5 cm and is several cm lower than that for observations of low-elevation satellites (except for the E5 and L2W observations). Figure 4: A model of the code multipath error as a function of satellite elevation for **(a)** Galileo and **(b)** GPS. Figure 3: Standard deviation of pseudorange noise versus elevation at the WUT2 site. Figure 2: Standard deviation of code multipath error versus elevation at the WUT2 site. Due to the local nature of the multipath effect, an important element of the analysis of the impact of this phenomenon is the examination of the spatial distribution of this error. Such an analysis makes it possible to identify the main directions, from which observations are particularly affected by signal reflections. This may allow us to eliminate from the environment objects that are potentially responsible for signal reflections or help to introduce an elevation mask, taking into account not only satellite elevation but also its direction. The spatial distribution of the multipath error, shown in Figure 5, is based on the horizontal coordinate grid with a mesh size of 30\({}^{\circ}\) for azimuth and 10\({}^{\circ}\) for elevation. The multipath STD values were visualized as dots, where both the color and size of the dot reflect the magnitude of the parameter. Due to the almost identical nature of all observations of a given GNSS system, the visualization was made only for E1C and L1 C/A signals. The obtained results confirm that the largest multipath errors are recorded for observations of satellites in the elevation range between 10 and 20\({}^{\circ}\).