Symmetry-Aware Vehicle State Estimation Using a Chaotic-Gradient-Optimized Extended Kalman Filter

To address the uncertainty of the measurement noise covariance matrix in vehicle state estimation, this paper proposes a symmetry-aware extended Kalman filter optimized by a chaotic-gradient strategy. The symmetry-aware concept is introduced from the approximate mirror symmetry of vehicle lateral dynamics under left and right steering excitations. Under identical road adhesion and vehicle operating conditions, the yaw-rate and sideslip-angle responses should exhibit balanced statistical characteristics for positive and negative lateral motions. However, a fixed measurement noise covariance matrix may break this balance and lead to direction-dependent estimation bias or delayed convergence. To improve the statistical consistency of the estimation process, the proposed method adaptively tunes the measurement noise covariance matrix according to the innovation covariance mismatch. A chaotic search mechanism is first used to enhance global exploration, and a variable-step gradient method is then applied to refine the local optimal solution. Through the iterative combination of chaotic traversal and gradient-based refinement, the proposed observer improves the balance between model prediction and measurement correction under stochastic disturbances. The effectiveness of the proposed method is verified through CarSim and MATLAB/Simulink co-simulation. The results show that, compared with EKF, UKF, and AEKF benchmark observers, the proposed CG_EKF provides more accurate estimation of vehicle yaw rate and sideslip angle.