###### Abstract  
Multipath effects can significantly reduce the accuracy of GNSS precise positioning. Traditional methods, such as sidereal filtering and grid-based approaches, attempt to model and mitigate these errors by leveraging the spatial autocorrelation of multipath based on residuals. However, these methods can only approximately handle spatial autocorrelation data, limiting their effectiveness. This study investigates the spatial cross-correlation of residuals between various GNSS frequency bands, analyzes their covariance function parameters, and evaluates the impact of constellation shifts on long-term multipath mitigation. Based on this, a simplified autocorrelation-based approach utilizing unified covariance parameters for multipath mitigation is proposed, with its efficacy assessed for both short- and long-term applications. The study demonstrates the correlation of multipath effects across various GPS and Galileo frequencies, including GPS L1/L2/L5 and Galileo E1/E5a/E5b/E5 ab/E6, by analyzing correlation coefficients. A strong correlation (greater than 0.8) is observed between residuals of closely spaced frequencies, such as E5b and E5 ab, despite their frequency differences. Additionally, the covariance parameters of the residuals are found to be consistent across all frequencies for a baseline, suggesting that unified parameters can be applied effectively for spatial autocorrelation-based multipath mitigation without sacrificing performance. The orbit shifts of certain GPS satellites, particularly G02, G20, and G21, result in significant changes in orbital parameters and satellite tracks, reducing the effectiveness of long-term multipath mitigation. However, the impact of GPS orbit shifts can be minimized through periodic model updates or by integrating GPS and Galileo modeling. In experiments, the LSC correction strategy based on a GPS/Galileo combination, utilizing unified parameters, outperforms the grid method based on the GPS/Galileo combination, improving the mean residual variance elimination rate by 11.3% for GPS L1 and 11.4% for Galileo E1. These improvements remain consistent, with rates of 11.3% and 15.7%, respectively, even on DOY 365, which is 327 days after the modeling data were collected. multi-GNSS; multipath; least-squares collocation; orbit shift; spatiotemporal correlation 2024 2  
The most straightforward way to mitigate multipath effects is by selecting observation environments that minimize reflections near the receiver antenna. However, this approach is often impractical, especially in complex environments. As a result, researchers have explored various methods to address multipath errors, including both hardware enhancements and software processing techniques. Hardware solutions typically focus on improving antenna designs to reduce multipath, such as using right-handed circular polarization antennas [2], choke ring antennas [3], helix antennas [4], and narrow correlator delay-locked loops [5]. While these approaches can lessen the impact of multipath, they are only partially effective and often come with significant costs. Software-based methods involve developing analytical or simulated models for calibration. These approaches include weighting GNSS observation data based on the signal-to-noise ratio [6; 7] or carrier-to-noise-power-density ratio [1; 8]. Additionally, multipath effects can be extracted or suppressed in the frequency domain using filtering techniques. Common methods include the Vondrak filter [9], wavelet analysis [10; 11], and the Kalman filter [12]. Additionally, two methods based on the spatiotemporal repeatability of multipath are commonly used for real-time mitigation in static or quasi-static environments. The first, known as the sidereal filtering (SF) method, exploits the near-daily repetition of GNSS satellite constellations. This repetition leads to recurring multipath effects on almost a daily basis, allowing residuals from post-processing to be applied to correct current measurements [13; 14; 15].