The escalating development of Maritime Autonomous Surface Ships (MASS) has imposed rigorous demands on the precision, continuity, and resilience of onboard integrated navigation systems. However, in complicated marine settings, data from the Global Navigation Satellite System (GNSS) and Doppler Velocity Log (DVL) are frequently corrupted by multipath effects and non-line-of-sight (NLOS) interference. These disturbances introduce anomalous observations that violate Gaussian noise assumptions, thereby severely deteriorating the robustness and estimation quality of traditional sliding-window factor graph optimization (SW-FGO). To mitigate this problem, this study introduces a novel integrated navigation strategy termed gradient-adaptive factor graph optimization (GA-FGO). By designing a gradient-adaptive robust objective function within the factor graph structure, the proposed method dynamically re-weights constraints from the inertial navigation system (INS), GNSS, and DVL. This mechanism adequately suppresses the influence of measurement outliers at the optimization level. Furthermore, a unified solution framework utilizing iterative reweighted least squares (IRLS) and the Gauss–Newton method is established to simultaneously perform adaptive weight updates and state estimation. Validation was based on offline field data benchmarked against the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and standard SW-FGO. The simulation results demonstrated that the GA-FGO algorithm achieves superior positioning accuracy and estimation stability under realistic measurement conditions.
Guo et al. (2026) studied this question.