Multipath Mitigation in Single-Frequency Multi-GNSS Tightly Combined Positioning via a Modified Multipath Hemispherical Map Method

Multipath is a source of error that limits the Global Navigation Satellite System (GNSS) positioning precision in short baselines. The tightly combined model between systems increases the number of observations and enhances the strength of the mathematical model owing to the continuous improvement in GNSS. Multipath mitigation of the multi-GNSS tightly combined model can improve the positioning precision in complex environments. Interoperability of the multipath hemispherical map (MHM) models of different systems can enhance the performance of the MHM model due to the small multipath differences in single overlapping frequencies. The adoption of advanced sidereal filtering (ASF) to model the multipath for each satellite brings computational challenges owing to the characteristics of the multi-constellation heterogeneity of different systems; the balance efficiency and precision become the key issues affecting the performance of the MHM model owing to the sparse characteristics of the satellite distribution. Therefore, we propose a modified MHM method to mitigate the multipath for single-frequency multi-GNSS tightly combined positioning. The method divides the hemispherical map into 36 x 9 grids at 10 degrees x 10 degrees resolution and then searches with the elevation angle and azimuth angle as independent variables to obtain the multipath value of the nearest point. We used the k-d tree to improve the search efficiency without affecting precision. Experiments show that the proposed method improves the mean precision over ASF by 10.20%, 10.77%, and 9.29% for GPS, BDS, and Galileo satellite single-difference residuals, respectively. The precision improvements of the modified MHM in the E, N, and U directions were 32.82%, 40.65%, and 31.97%, respectively. The modified MHM exhibits greater performance and behaves more consistently.