PINNARX: A Physics-Informed Framework for Resilient Inertial Navigation in GNSS-Denied Environments

Accurate navigation in Global Navigation Satellite System (GNSS)-denied environments remains a major challenge due to inertial sensor noise and signal loss. This paper introduces a physics-informed Nonlinear Autoregressive Exogenous (PINNARX) neural network framework to enhance the performance of inertial measurement units (IMUs) utilizing low-cost inertial and enable robust navigation and enable robust navigation. By embedding physical constraints into the learning process—including acceleration consistency, angular rate fidelity, and temporal smoothness—the proposed method improves the quality of the raw sensor measurements before fusion with GNSS signals. An ablation study is conducted on the PINNARX model to quantitatively assess the individual contributions of the physical loss functions, optimizer choices, and delay configurations to the overall performance. The improved and physically-consistent IMU data is integrated via a Reduced Inertial Sensor System (RISS) and an Extended Kalman Filter (EKF), providing robust performance during GNSS outages. Experimental validation over real-world trajectories shows substantial improvements in positioning and orientation accuracy compared to baseline and artificial intelligence (AI)- enhanced approaches. Specifically, the proposed system reduces the two-dimensional position root-mean-square error (RMSE) by up to 70.3%; furthermore, the azimuth estimation accuracy increases by up to 87.3%, with improvements in both eastward and northward velocity estimates.