An Improved Factor Graph Optimization Algorithm Enhanced with ANFIS for Ship GNSS/DR Integrated Navigation

Accurate and reliable positioning is essential for unmanned marine vehicles (UMVs), especially in complex maritime environments. Existing algorithms often underutilize historical information, struggle with nonlinear dynamics, and lack adaptability in the GNSS Measurement Noise Covariance, leading to degraded performance. This study proposes an enhanced Factor Graph Optimization (FGO) method integrated with an adaptive neuro-fuzzy inference system (ANFIS) to overcome these challenges. First, an improved GNSS/Dead Reckoning (DR) factor graph is built using refined error models to enhance baseline accuracy. Second, a marginalization factor is introduced utilizing a sliding window and the Schur complement method to retain informative historical data while reducing computational load, thereby improving stability and field performance. Third, an ANFIS-based adaptive GNSS factor dynamically updates the GNSS Measurement Noise Covariance Matrix (GMNCM) to strengthen robustness under variable maritime conditions. Simulation and field tests demonstrate significant improvements: the proposed method achieves 29.1%, 26.5%, and 9.9% higher accuracy than EKF, UKF, and conventional FGO, respctively. Under GNSS interruptions, EKF and UKF diverge with errors exceeding 500 m, while FGO limits drift to 20 m. The proposed ANFIS–FGO shows the smallest fluctuations and fastest recovery, confirming its strong resilience and practical applicability for UMV navigation.