HTAGN-Enhanced Factor Graph Optimization for Shipborne GNSS/INS/Gyrocompass Integrated Navigation

Shipborne Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) integrated navigation based on Factor Graph Optimization (FGO) is increasingly used for maritime positioning, but its performance can be limited in low-dynamic sailing scenarios. In conventional GNSS/INS FGO without direct heading measurements, the heading state is mainly propagated by inertial measurements. During prolonged straight-line or low-maneuver sailing, position-related constraints provide only weak heading correction, which may lead to cumulative heading errors. In addition, existing learning-based GNSS outage compensation methods often introduce pseudo-GNSS observations with fixed covariance, making it difficult to represent the direction-dependent and time-varying uncertainty of data-driven predictions. To address these issues, this paper proposes a heteroscedastic TCN-Assisted GRU Network (HTAGN)-enhanced FGO framework for shipborne GNSS/INS/gyrocompass integrated navigation. Within the unified framework, a gyrocompass heading factor is constructed to provide persistent GNSS-independent heading constraints, and an HTAGN is designed to generate pseudo-GNSS position increments during GNSS outages. The direction-dependent standard deviations predicted by HTAGN are further mapped to the covariance matrix of pseudo-GNSS position factors, enabling confidence-adaptive factor weighting in the optimization process. The framework was validated on a single real-world sea trial with artificially simulated GNSS outages. The gyrocompass heading factor reduced the heading Root Mean Square Error (RMSE) by 84.6% compared with conventional GNSS/INS FGO. During 90 s and 180 s outages, the proposed method reduced the horizontal positioning RMSE by 63.7% and 52.5%, respectively, relative to the fixed-covariance TAGN baseline, demonstrating improved heading estimation and short-term positioning continuity under the tested conditions.