An Adaptive Robust EKF Based on Mahalanobis Distance and Non-Holonomic Constraints for Enhancing Vehicle Positioning Accuracy

This article introduces a novel approach in the field of tightly coupled global navigation satellite system (GNSS)/inertial navigation system (INS) integration, aimed at substantially reducing positioning errors. We propose an innovative adaptive robust extended Kalman filter (AREKF), termed MAREKF, which utilizes the Mahalanobis distance (MD) to effectively mitigate the challenges posed by strong system nonlinearity and modeling errors, thereby enhancing vehicle positioning accuracy. Traditional AREKF methods, including the proposed MAREKF, often struggle with the identification of gross errors in measurement data and may exhibit imbalances in parameter adjustments. To overcome these challenges, we propose the non-holonomic constraint (NHC)-driven MAREKF (NMAREKF), integrating NHC conditions to enhance adaptability and robustness in nonlinear environments. The NMAREKF shows a significant improvement in the filtering process and system stability. The empirical evaluation, using datasets from diverse environments, focuses on performance metrics such as root mean square error (RMSE) and average standard deviation (ASD) of position, velocity, and attitude. The results demonstrate that NMAREKF outperforms existing methods in handling kinematic and measurement model errors. The NMAREKF method, blending NHC and MD, emerges as a promising solution for reducing positioning errors in complex navigation scenarios, offering significant theoretical and practical advancements in the field of precision positioning.