Multi-Kernel Bandwidth Based Maximum Correntropy Extended Kalman Filter for GPS Navigation

The extended Kalman filter (EKF) is extensively applied in integrated navigation systems that combine the global navigation satellite system (GNSS) and strap-down inertial navigation system (SINS). However, the performance of the EKF can be severely impacted by non-Gaussian noise and measurement noise uncertainties, making it difficult to achieve optimal GNSS/INS integration. Dealing with non-Gaussian noise remains a significant challenge in filter development today. Therefore, the maximum correntropy criterion (MCC) is utilized in EKFs to manage heavytailed measurement noise. However, its capability to handle non-Gaussian process noise and unknown disturbances remains largely unexplored. In this paper, we extend correntropy from using a single kernel to a multi-kernel approach. This leads to the development of a multi-kernel maximum correntropy extended Kalman filter (MKMC-EKF), which is designed to effectively manage multivariate non-Gaussian noise and disturbances. Further, theoretical analysis, including advanced stability proofs, can enhance understanding, while hybrid approaches integrating MKMC-EKF with particle filters may improve performance in nonlinear systems. The MKMC-EKF enhances estimation accuracy using a multi-kernel bandwidth approach. As bandwidth increases, the filter's sensitivity to non-Gaussian features decreases, and its behavior progressively approximates that of the iterated EKF. The proposed approach for enhancing positioning in navigation is validated through performance evaluations, which demonstrate its practical applications in real-world systems like GPS navigation and measuring radar targets.