## 3 Computation and Analysis
### Unified Covariance Function Parameters for Short and Long-Term Multipath Correction Analysis
On DOY 339, the re-modeled LSC_E strategy matches the pre-re-modeling performance of \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**DOY of 2023**} \\ \cline{2-13}  & **039** & **069** & **099** & **129** & **159** & **189** & **219** & **249** & **279** & **309** & **339** & **365** \\ \hline Uncalibrated & 4.12 & 4.10 & 4.46 & 4.20 & 4.09 & 4.44 & 4.56 & 4.45 & 4.65 & 4.65 & 4.89 & 5.09 \\ Grid\_E & 2.46 & 2.45 & 2.66 & 2.66 & 2.51 & 2.71 & 2.95 & 2.76 & 2.86 & 2.74 & 3.04 & 3.56 \\ Grid\_GE & 2.49 & 2.46 & 2.68 & 2.64 & 2.56 & 2.71 & 2.95 & 2.70 & 2.87 & 2.75 & 3.03 & 3.59 \\ LSC\_E & 2.05 & 2.07 & 2.23 & 2.28 & 2.18 & 2.30 & 2.59 & 2.37 & 2.49 & 2.33 & 2.63 & 3.04 \\ LSC\_GE & 2.02 & 2.05 & 2.18 & 2.24 & 2.17 & 2.27 & 2.57 & 2.32 & 2.45 & 2.29 & 2.52 & 2.97 \\ Grid\_E (remodel) & & & & & & & & 2.51 & 2.71 & 2.60 & 2.96 & 3.58 \\ Grid\_GE (remodel) & & & & & & & & & 2.54 & 2.74 & 2.64 & 2.98 & 3.51 \\ LSC\_E (remodel) & & & & & & & & & 2.07 & 2.31 & 2.16 & 2.48 & 3.16 \\ LSC\_GE (remodel) & & & & & & & & & 2.04 & 2.27 & 2.14 & 2.47 & 3.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: STDs of the SD residuals before and after multipath calibration for Galileo E1 (unit: mm). \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**DOY of 2023**} \\ \cline{2-13}  & **039** & **069** & **099** & **129** & **159** & **189** & **219** & **249** & **279** & **309** & **339** & **365** \\ \hline Uncalibrated & 5.14 & 5.38 & 5.31 & 5.12 & 5.12 & 5.17 & 5.76 & 5.63 & 5.75 & 5.59 & 5.85 & 5.66 \\ Grid\_G & 2.97 & 3.67 & 3.99 & 4.08 & 4.08 & 4.15 & 4.71 & 4.48 & 4.61 & 4.47 & 4.62 & 4.66 \\ Grid\_GE & 2.96 & 3.34 & 3.53 & 3.52 & 3.55 & 3.52 & 4.18 & 3.91 & 4.05 & 3.83 & 3.88 & 3.97 \\ LSC\_G & 2.43 & 3.02 & 3.46 & 3.41 & 3.54 & 3.72 & 4.2 the LSC_GE strategy, but it falls short after this period. The re-modeled LSC_GE strategy maintains similar performance to the pre-re-modeling performance of the LSC_GE. Kinematic mode processing of GPS L1 and Galileo E1 data was conducted using the outlined strategies, with the results presented in Figure 21. The LAMBDA method was employed for ambiguity estimation in the processing, and the ambiguity fixing rates were over 99%. This figure displays the root mean square (RMS) values for the North, East, and Up components before and after multipath calibration. The combined GPS/Galileo solution for GPS L1 provided better results than the GPS-only solution. For Galileo E1, the combined solution was on par with the Galileo-only solution. Across both frequencies, the autocorrelation-based LSC using unified covariance function parameters yielded lower RMS errors and enhanced positioning accuracy compared to the grid method, indicating its efficacy whether applied to combined or single-system data. Figure 21: RMS of displacements of the North, East, and Up components of the baseline MAT1_MATE for GPS L1 (**a**) and Galileo E1 (**b**) using different correction strategies. Figure 20: SD residual variance reduction rates of the baseline MAT1_MATE for GPS L1 (**a**) and Galileo E1 (**b**) by the grid method and the autocorrelation-based LSC method.