## 4 Results  
Multipath error significantly affects the accuracy of GNSS precise positioning but can be effectively mitigated using spatial autocorrelation-based methods in static and quasi-static environments. Traditional techniques like sidereal filtering and grid-based approaches only approximate the handling of spatial autocorrelation data. However, the spatiotemporal correlations of multipath can be more accurately modeled by utilizing the covariance function. This study investigates the spatial cross-correlation between different frequency bands across various GNSS systems, along with spatial autocorrelation function parameters and the effects of constellation shifts, to simplify autocorrelation-based methods like Least-Squares Collocation and enhance long-term performance. The results reveal that overlapping frequencies, such as L1/E1 and L5/E5a, show very strong correlations, while non-overlapping frequencies, such as L2 and E5b, also exhibit strong correlations, with coefficients exceeding 0.8. The covariance function parameters, typically including the residual variance and the range parameter that control the rate of correlation decay with distance, remain relatively consistent across frequencies. This consistency allows autocorrelation-based methods using unified covariance function parameters to achieve a variance reduction rate (VRR) comparable to methods that rely on frequency-specific covariance function parameters. Additionally, the GPS satellites G02, G20, and G21 exhibit noticeable orbit shifts, leading to significant changes in orbital parameters and satellite tracks, which diminishes the effectiveness of long-term multipath mitigation. These satellites display larger average deviations, reaching a maximum deviation of 0.029 rad. In contrast, the Galileo satellites demonstrate more stable orbits, with fluctuations confined to 0.004 rad. When combining GPS and Galileo reference orbits, the maximum deviation for GPS satellites reduces to 0.003 rad, and the orbital repeat rate stabilizes at 100%. Multipath mitigation experiments using both the grid method and the autocorrelation-based LSC with a unified covariance function for GPS L1 and Galileo E1 frequencies on the MATE_MAT1 baseline were conducted. This analysis considers the GPS, Galileo, and combined GPS/Galileo data separately. For GPS L1, the LSC_GE strategy improves the residual variance reduction rate by 0.13%, 11.05%, and 11.16% compared to LSC_G, Grid_GE, and Grid_G, respectively, on DOY 039, the first day after modeling. These improvements increase to 14.24%, 11.25%, and 29.59% on DOY 365, 327 days from the modeling data. Similarly, for Galileo E1, the LSC_GE strategy shows improvements of 0.75%, 12.27%, and 11.58% on the first day following modeling, rising to 1.5%, 15.69%, and 14.96% by DOY 365. As a result, the accuracy of kinematic positioning is improved. Overall, the unified covariance function proves effective for autocorrelation-based multipath mitigation, outperforming conventional grid methods. Although GPS orbit drift negatively affects long-term mitigation, integrating GPS and Galileo data consistently produces lower RMS values and more accurate baseline solutions, significantly mitigating the impact of orbit drift. However, the method is based on spatial autocorrelation. Therefore, in the case that the spatial autocorrelation is low, the performance will be limited. This may happen in complex multipath environments. However, this need to be tested when complex multipath environments are encountered in practice. Conceptualization, W.X. and Y.T. ; methodology, W.X. and Y.T. ; software, W.X. and Y.T. ; validation, X.D. and Q.Z. ; formal analysis, Y.L. and X.D. ; investigation, X.R. ; writing--original draft preparation, W.X. ; writing--review and editing, Y.T. and Q.Z. ; visualization, Y.L. and X.R. ; supervision, Y.T. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 42274032.