## 3 Computation and Analysis
### Correlation Analysis Between GPS/Galileo Frequencies  
The carrier phase SD residual distribution for all frequencies of the MATE_MAT1 and KERG_KRGG baselines over the 10-day period from DOY 029-038 in 2023 is presented in Figures 5 and 6. The SD residuals for satellites at low elevation angles (below \(30^{\circ}\)) are relatively large, a common feature associated with the heightened multipath effects in this region [36]. Additionally, it is noted that the number of satellites observed at the E5a frequency for the KERG_KRGG baseline is relatively low when the elevation angle is below \(15^{\circ}\). This reduction is primarily due to the lack of low-elevation satellite data at the KERG station for this frequency. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Frequency (MHz)**} & \multicolumn{2}{c}{**Signal**} & \multicolumn{2}{c}{**Baselines**} \\ \cline{2-5}  & **GPS** & **Galileo** & **MATE\_MAT1** & **KERG\_KRGG** \\ \hline
1575.420 & L1 & E1 & \(\surd\) & \(\surd\) \\
1278.750 & & E6 & \(\times\) & \(\surd\) \\
1227.600 & L2 & & \(\surd\) & \(\surd\) \\
1207.140 & & E5b & \(\surd\) & \(\surd\) \\
1191.795 & & E5 ab * & \(\surd\) & \(\surd\) \\
1176.450 & L5 & E5a & \(\surd\) & \(\surd\) \\ \hline \end{tabular}  
* i.e., E5(E5a + E5b).  
\end{table} 
Table 1: The frequency values of the available open service signals transmitted by GPS and Galileo for the two baselines. “\(\surd\)” means that the baseline has this frequency, and “\(\times\)” means that the baseline does not. Figure 4: Multipath distributions for the baselines MATE_MAT1 (**a**) and KERG_KRGG (**b**). The red boxed area in (**a**) represents the significant multipath errors of the MATE_MAT1 baseline around an elevation angle of \(20^{\circ}\) toward the southeast. The residuals for the GPS L1/L2/L5 and Galileo E1/E5b/E5 ab frequencies over a 10-day period, as the satellites traversed a designated square window, are presented in Figure 7, offering a comparative view of the signal variations across different GNSS frequencies. The windows for the MATE_MAT1 baseline cover an elevation angle of 7\({}^{\circ}\) to 17\({}^{\circ}\) and an azimuth angle of 90\({}^{\circ}\) to 100\({}^{\circ}\), while for the KERG_KRGG baseline, the range is 7\({}^{\circ}\) to 17\({}^{\circ}\) in elevation and 140\({}^{\circ}\) to 150\({}^{\circ}\) in azimuth. A consistent pattern is observed for different frequencies at the same spatial locations. Notably, for overlapping or closely spaced frequencies, the satellite trajectory colors appear similar or nearly identical. For instance, this applies to overlapping frequencies such as GPS L1 and Galileo E1, closely spaced frequencies like GPS L2 and Galileo E5b, as well as GPS L5 and Galileo E5 ab, all of which follow the same pattern. In contrast, for frequencies with larger differences, such as GPS L1 and Galileo E5b/E5 ab, the trajectory colors vary significantly, and in some instances, even exhibit opposite sign values. Figure 5: Satellite tracks and SD residuals for all frequencies of the baseline MATE_MAT1 on DOY 029–038 of 2023. Figure 6: Satellite tracks and SD residuals for all frequencies of the baseline KERG_KRGG on DOY 029–038 of 2023. Figure 7: SD residuals for different frequencies of the MATE_MAT1 baseline ((**a–f**), 7\({}^{\circ}\)–17\({}^{\circ}\) in elevation and 90\({}^{\circ}\)–100\({}^{\circ}\) in azimuth) and the KERG_KRGG baseline ((**A–F**), 7\({}^{\circ}\)–17\({}^{\circ}\) in elevation and 140\({}^{\circ}\)–150\({}^{\circ}\) in azimuth). The Pearson correlation coefficient is used to evaluate the correlation between the residual sequences of any two frequencies. The absolute values of the resulting correlation coefficients are displayed in Figure 8, showing diagonal symmetry along the value of 1. To better visualize the strength of multipath error correlations between frequency pairs, a color gradient is applied, ranging from dark (strong correlation) to light (weak correlation).