BDSBAS/MSAS Fusion Positioning Algorithm Based on Sliding Window Variance Component Estimation Enhanced by Feedforward Neural Network and Factor Graph Optimization

Abstract To address the limitation of positioning accuracy in single Satellite-Based Augmentation Systems (SBAS) imposed by regional service performance, this paper proposes a BeiDou Satellite-Based Augmentation System (BDSBAS)/Multifunctional Satellite Augmentation System (MSAS) fusion positioning algorithm based on Sliding Window Variance Component Estimation (SW-VCE) enhanced by Feedforward Neural Network (FNN) and Factor Graph Optimization (FGO). First, SW-VCE is employed to estimate the positioning variance of each system in real time. Combined with Median Absolute Deviation robust estimation and the Huber weighting function, robust adaptive weighted fusion is achieved. Second, a 12dimensional quality feature vector is constructed, comprising six basic statistical features and six system-consistency and spatio-temporal evolution features, to train an FNN that learns the nonlinear mapping from quality features to fusion weight correction factors. Third, FGO is introduced to perform global optimization over the temporal position sequence through modeling with observation factors and smoothing factors, together with the Huber robust kernel function. Finally, the algorithm is validated through static tests at IGS stations BJFS and SEJN as well as a vehicle-borne dynamic test in an urban environment in Qingdao. Experimental results show that in static testing, the SW-VCE+FNN+FGO fusion algorithm improves positioning accuracy by an average of 41.1% over the single-system BDSBAS solution, 41.6% over the single-system MSAS solution, and 26.4% over the Position Domain Integration (PDI) method. In dynamic testing, the fusion algorithm achieves improvements of 36.8% over BDSBAS, 24.3% over MSAS, and 19.4% over PDI, confirming the effectiveness and robustness of the proposed algorithm under both static and dynamic scenarios.