PINK-GINS: A Hybrid Physics-Informed Neural Network and Kalman Filter Framework for GNSS/INS Tightly Coupled Integration

Global Navigation Satellite Systems (GNSS) integrated with Inertial Navigation Systems (INS) provide continuous positioning, but performance degrades with inaccurate noise modeling and cubic error growth during GNSS outages, particularly with lowcost Micro-ElectroMechanical Systems (MEMS) Inertial Measurement Units (IMUs). This paper presents PINK-GINS, a tightly coupled GNSS/INS framework that augments an Error-State Kalman filter (ESKF) with a Physics-Informed Neural Network (PINN). A dual-branch encoder extracts latent features from IMU sequences and GNSS indicators, which are fused through a gating mechanism to adaptively predict sensor biases and process and measurement noise covariances. Physics-constrained residuals are injected as soft pseudo-measurements to enforce strapdown consistency. When GNSS signals are reliable, adaptive noise covariance modeling enhances ESKF consistency, and under degraded or unavailable GNSS conditions bias correction and process noise adaptation mitigate inertial drift to enable robust dead reckoning. Real-world experiments with MEMS-grade IMUs across opensky, treeline, urban, and outage scenarios demonstrate that PINK-GINS consistently outperforms representative baselines and delivers improved accuracy and robustness under diverse conditions.