Robust fixed-point Kalman smoother for bilinear state-space systems with non-Gaussian noise and parametric uncertainties

Abstract

Kalman smoother is an effective algorithm to estimate the state of the dynamic systems with Gaussian noise. However, when the system is affected by non-Gaussian noise, the traditional Kalman smoother may suffer severe performance degradation, since it is derived from the minimum mean square error criterion. By introducing the maximum correntropy criterion, which accounts for all higher order moments and has the ability to resist non-Gaussian noise, this article studies the state estimation problem of the bilinear state-space system with non-Gaussian noises and parametric uncertainties. The bilinear system with parametric uncertainties is transformed into a linear time-varying system, and a robust fixed-point Kalman filter algorithm is derived based on the Cauchy kernel-based correntropy criterion. To improve the state estimation accuracy, a Cauchy kernel-based fixed-point Kalman smoother (CK-FPKS) algorithm is presented by introducing the backward smoothing. Simulation results show the effectiveness of the proposed algorithm.