Physics-Constrained Neural Covariance Estimation for High-Dynamic SINS/GNSS Integrated Navigation

Abstract

The accuracy and consistency of error-state Kalman filtering for SINS/GNSS integrated navigation depend critically on properly tuned process and measurement noise covariance matrices. In dynamic operation, these covariances can be non-stationary: inertial uncertainty changes with maneuver intensity, vibration, and sensor-bias instability, whereas GNSS measurement quality changes with satellite geometry, multipath, obstruction, and signal loss. Fixed-covariance and classical adaptive filters can therefore become overconfident or insufficiently responsive during abrupt maneuvers and degraded GNSS reception. We propose a physics-informed constrained neural covariance estimation (PC-NCE) framework that augments, rather than replaces, the error-state Kalman filter (ESKF) by estimating bounded process and measurement covariance-scale parameters online. The framework maps IMU-window sequences, GNSS-quality indicators, innovation statistics, and motion-state descriptors through a CNN-BiLSTM-attention network to filter-admissible Qk and Rk parameterizations injected into a closed-loop ESKF. Training enforces positivity, bounds, temporal smoothness, and innovation–consistency regularization. In a reproducible filter-level MATLAB scenario suite, PC-NCE improved covariance-scale tracking and selected consistency ratios relative to fixed and unconstrained neural baselines, whereas position RMSE gains were scenario-dependent. These results provide a simulation-level proof of concept supplemented by an initial held-out measured-trajectory evaluation; broader validation using a full 15-state SINS/GNSS implementation and additional field datasets remains necessary. By treating neural networks as uncertainty-perception layers rather than black-box state estimators, PC-NCE retains the interpretability and engineering safeguards of classical Kalman filtering.