An SVD-Based Observation Matrix Reconstruction and Dynamic Weighting Algorithm for Enhanced Multi-GNSS Differential Positioning Accuracy

Currently, over 100 Global Navigation Satellite System(GNSS) satellites are operational in orbit worldwide. GNSS observation equipment can simultaneously receive data from multiple navigation systems within the near-Earth space environment. However, due to variations in receiver performance and environmental conditions, the number of visible satellites and available frequencies from each system exhibits significant temporal variability. Existing multi-system, multi-frequency carrier-phase differential processing algorithms often adopt equal-weight strategies, failing to account for the heterogeneous quality of observations across systems and frequencies. Moreover, equal-weighted methods struggle with double-differenced models due to dimensional inconsistencies among system-specific design matrices.To address these limitations, this study proposes a Singular Value Decomposition (SVD)-based matrix dimension reconstruction algorithm for real-time multi-GNSS differential processing. The proposed method first utilizes an SVD-based reconstruction mechanism to standardize the column dimensions of observation matrices across systems, thereby eliminating fusion barriers caused by dimensional mismatches. Subsequently, Helmert variance component estimation is introduced to dynamically optimize the weights among multi-GNSS systems, enabling robust and high-precision fusion of heterogeneous GNSS observations. Experimental validation using datasets from BDS, GPS, and GLONASS confirms the method's effectiveness. In static scenarios, the algorithm improves positioning accuracy by at least 26.81% and enhances solution stability by 14.45% for single-frequency observations. For multi-frequency data, accuracy and stability improvements exceed 20.66% and 10.92%, respectively. Under kinematic conditions, the method effectively suppresses observation fluctuations and boosts precision, particularly excelling in single-frequency processing. Overall, the SVD-based weighted optimization algorithm demonstrates strong applicability to both single- and multi-frequency GNSS data, offering significant benefits for high-precision navigation in complex environments.