TriMSAN: A Triple-Path Multi-Modal Self-Attention Network for Tightly Coupled GNSS/INS Integration Under GNSS Outages

The GNSS/INS integrated navigation framework is widely used in urban environments. In obstructed environments, GNSS outages force the system to rely solely on INS and cause rapid error growth. Most learning-based methods predict navigation states rather than the satellite-wise observations required by tightly coupled filtering. This paper proposes TriMSAN, a per-satellite observation-domain framework that predicts pseudorange and pseudorange-rate variations from IMU/INS motion features, ephemeris-derived satellite kinematics and historical GNSS observations. Branch-wise transformer encoders, cross-modal interaction and modality-attention fusion are used to extract and fuse these features. The predicted variations are recursively accumulated to reconstruct satellite-wise pseudo-measurements and injected into the original tightly coupled filter. In four 60 s simulated outages, TriMSAN achieved an overall three-dimensional positioning RMSE of 5.051 m and lower pseudorange and pseudorange-rate prediction errors than MHSA. On the GREAT Dataset, cross-trajectory evaluation using two injected 90 s complete outages yielded an overall horizontal positioning RMSE of 15.506 m for TriMSAN, compared with 23.253 m for MHSA and 123.358 m for INS propagation. Controlled partial and time-varying satellite-availability experiments further evaluated the joint use of reconstructed and retained real observations. These results support per-satellite multi-modal observation-domain prediction for tightly coupled GNSS/INS integration under the evaluated GNSS outage conditions.