Motion Estimation Algorithm Based on GA-Optimized High-Order Extended Kalman Filter

To address the limitations of the Extended Kalman Filter (EKF) in handling strongly nonlinear systems, such as low accuracy, significant errors in robotic motion estimation, weak anti-interference capabilities, and sub-optimal performance in vehicle motion estimation, this paper introduces a novel vehicle motion estimation method based on a Genetic Algorithm-Optimized Higher Order Extended Kalman Filter (GA-HEKF). The HEKF algorithm enhances traditional EKF by incorporating hidden variables to mitigate round-off errors and pseudo-linearizing the vehicle motion model. This approach establishes a linear relationship between system variables and hidden variables, transforming the system state model into a linear form and equivalently rewriting the observation model. As a result, the vehicle motion model is reformulated into a structure compatible with Kalman filtering, enabling more accurate state estimation. To further improve the performance of the HEKF algorithm, an improved genetic algorithm is employed to optimize the covariance matrices of system noise and observation noise during the high-order extended Kalman filtering process. This optimization enhances the precision of vehicle state parameter estimation by dynamically adjusting the noise characteristics to better reflect real-world conditions. Simulation experiments are conducted to validate the effectiveness of the proposed method. The results demonstrate that the GA-HEKF algorithm outperforms traditional EKF in terms of accuracy, robustness, and computational efficiency. Specifically, it exhibits superior performance in scenarios with high nonlinearity and noise interference, making it a promising solution for advanced vehicle motion estimation applications. The proposed method not only addresses the inherent limitations of EKF but also provides a framework for improving state estimation in other complex nonlinear systems.