SINDy-Based Motion-Dependent Nonholonomic Constraint Covariance Adaptation for GNSS-Denied MEMS/INS Vehicle Navigation

Low-cost microelectromechanical-system inertial measurement units (MEMS IMUs) enable self-contained vehicle navigation, but their errors accumulate rapidly when global navigation satellite system (GNSS) updates are unavailable. Nonholonomic constraints (NHC) can limit this drift without external sensors, but a fixed pseudo-measurement covariance becomes inconsistent during dynamic vehicle motion. This paper presents a SINDy-inspired method for motion-dependent NHC covariance adaptation. The method preserves NHC geometry and uses completed causal IMU windows to identify a sparse relation between vehicle motion and the conditional second moment of the lateral and vertical NHC residuals. The prediction is converted into a bounded positive pseudo-measurement covariance for an invariant extended Kalman filter (InEKF). A bounded vertical covariance correction and a positive-semidefinite process-noise gate represent residual uncertainty. The learned modules output covariance quantities only, while the InEKF remains the sole estimator of navigation states. Under a strict complete-GNSS-denial protocol, the method was evaluated on three held-out vehicle sequences using route-exclusive training. Relative to fixed NHC, the 3-D position RMSE decreased from 4.135 to 1.283 m on sequence 0027 and from 14.456 to 4.293 m on sequence 0033. These reductions were 68.96% and 70.30%, respectively, and the event-level violation-induced correction score decreased by 94.41%. On the additional independent holdout sequence 0034, the proposed method reduced the 3-D position RMSE from 6.735 m with fixed NHC to 3.929 m, corresponding to a reduction of 41.67%. The results indicate that causal, motion-dependent covariance adaptation can regulate NHC information in the evaluated vehicle inertial-navigation setting.