Nonlinear Regressive Maximum Correntropy Extended Kalman Filter With Students t-Kernel for GPS Navigation

Abstract

State estimation is a critical task across many disciplines, with the extended Kalman filter (EKF) being a widely adopted solution. However, the EKF is built on the mean square error criterion, which limits it to capturing only second-order noise statistics, making it vulnerable to significant performance drops in the presence of outliers. In practical engineering scenarios, noise often deviates from a Gaussian distribution, and outliers naturally occur, further complicating the estimation process. To overcome these challenges, this study proposes a novel filtering method, the Student's t kernel-based nonlinear regressive maximum correntropy extended Kalman filter, which is robust to non-Gaussian noise and outliers. Additionally, the algorithm's convergence is examined due to its reliance on a fixed-point iteration approach to derive the optimal state estimate. The robustness for the proposed method has been verified in various noise scenario and dynamic conditions. Performance evaluations through various error technique demonstrate the effectiveness of the proposed method in improving GPS positioning accuracy, highlighting its broader applicability in real-world systems such as GPS navigation and radar-based measurements.