An extended Kalman filter with mixture kernel maximum correntropy criterion for GPS navigation applications

Abstract

For enhancing the robustness of the Kalman filter in the presence of non-Gaussian noise or measurement outliers within a nonlinear state-space model, a robust filter based on mixed correlation entropy is proposed in this paper. The mixed correlation entropy cost function is utilized as a replacement for the second-order function used in the Kalman filter for measurement fitting errors in the Global Positioning System (GPS). Leveraging entropy theory with kernel functions, a novel robust filtering algorithm is designed by using the maximum correntropy criterion (MCC). While it has been demonstrated, the MCC-based robust filters are feasible for handling non-Gaussian noise and the default kernel in the original MCC, such as the Gaussian kernel, which may not be sufficient for dealing with more complex data encountered in many practical problems. The selection of kernel parameters for MCC-based filters becomes challenging when an adaptive kernel is not used. Therefore, there is a need to design algorithms, which are insensitive to kernel parameters for handling the measurement outliers. In this paper, the robust filters based on double-Gaussian mixture correntropy are proposed and combined with the nonlinear filtering algorithms, replacing filtering methods that rely solely on the minimum mean square criterion. Finally, the algorithm's robustness is validated through simulation experiments under a certain degree of accuracy. The solutions suggested may outperform the current robust approaches, according to simulation findings, which can achieve better performance for GPS navigation applications.