A novel fractional nonlinear state estimation algorithm in non-Gaussian noise environment

Abstract

This paper presents research on state estimation for nonlinear fractional-order systems in non-Gaussian noise. Traditional estimation methods based on the minimum mean square error criterion perform poorly for fractional-order systems in non-Gaussian noise Using the Bayesian filtering framework and information theoretic learning, a novel fractional central difference Kalman filter based on the maximum correntropy criterion is firstly proposed and named MC-FCDKF. The proposed MC-FCDKF contains prior state update step, regression model construction and posterior state update step. The regular Taylor series expansion is replaced by the Stirling interpolation technique. The conventional measurement prediction and the associated calculation of covariances are also eliminated, enhancing practicality and real-time performance. Finally, the performance of the proposed algorithm is compared with several other algorithms through lithium battery state-of-charge estimation to verify the effectiveness and benefits under non-Gaussian noise perturbation.