Maximum Correntropy High-Order Extended Kalman Filter

Abstract

In this paper, a novel maximum correntropy high-order extended Kalman filter (H-MCEKF) is proposed for a class of nonlinear non-Gaussian systems presented by polynomial form. All high-order polynomial terms in the state model are defined as implicit variables and regarded as parameter variables; the original state model is equivalently formulated into a pseudo-linear form with original variables and parameter variables; the dynamic relationship between each implicit variable and all variables is modeled, then an augmented linear state model appears by combing with pseudo-linear state model; similarly, the nonlinear measurement model can be equivalently rewritten into linear form; once again, the statistical characteristics of non-Gaussian modeling error are described by mean value and variance based on their finite samples; combing original measurement model with predicted value regarded as added state measurement, a cost function to solve the state estimation based on maximum correntropy criterion (MCC) is constructed; on the basis of this cost function, the state estimation problem can be equivalently converted into a recursive solution problem in the form of Kalman filter, in which the filter gain matrix is solved by numerical iteration though its fixed-point equation; illustration examples are presented to demonstrate the effectiveness of the new algorithm.