Integrated GNSS/LEO precise point positioning using factor graph optimization with heterogeneous graph-based stochastic modeling

Abstract Low Earth Orbit (LEO) satellite augmentation can improve the availability and satellite geometry of Precise Point Positioning (PPP). However, most existing Global Navigation Satellite System (GNSS)/LEO PPP methods rely on fixed stochastic models and do not fully exploit the heterogeneous characteristics of GNSS and LEO observations, a limitation that is particularly problematic in complex environments. To address this limitation, we propose a Factor Graph Optimization (FGO)-based approach for integrated GNSS/LEO PPP that combines heterogeneous observation modeling with an adaptive stochastic model. We formulate a unified dual-frequency PPP-FGO framework to process both GNSS and LEO observations. A relation-aware Heterogeneous Graph Neural Network (HetGNN) is designed to jointly model receiver, GNSS satellite, and LEO satellite nodes and their multitype observation relationships. This network estimates observation-level uncertainty scale factors, which are incorporated into the adaptive stochastic model through covariance rescaling. We evaluate the proposed method using real vehicular GNSS data and simulated LEO observations in mixed, open, and urban obstructed scenarios. The proposed approach achieves average Three-Dimensional (3D) positioning Root Mean Square (RMS) errors of 3.06 m, 0.67 m, and 3.00 m in these respective environments. In the long-distance mixed scenario, it also achieves an availability rate of 98.93% and a 60-s continuity probability of 91.09%. Compared to baseline methods using elevation-angle and carrier-to-noise-density-ratio joint weighting and residual-driven weighting, the proposed method improves 3D positioning accuracy in the urban obstructed scenario by 28.4% and 10.2%, respectively, while reducing the reconvergence time to 47.33 s. The proposed method improves positioning accuracy, availability, short-term continuity, and reconvergence speed for GNSS/LEO PPP in complex environments, offering a promising approach for reliable, high-accuracy positioning and navigation services.