Adaptive Cubature Kalman Filter Based on the Expectation-Maximization Algorithm

Weidong Zhou,Lu Liu

doi:10.1109/access.2019.2950227

Abstract

A cubature Kalman filter is considered to be one of the most useful methods for nonlinear systems. However, when the statistical characteristics of noise are unknown, the estimation accuracy is degraded. Therefore, an adaptive square-root cubature Kalman filter (ASCKF) is designed to handle the unknown noise. The maximum likelihood criterion and expectation-maximization algorithm are employed to adaptively estimate the parameters of unknown noise, thus restraining the disturbance resulting from unknown noise and improving the estimation accuracy. The stability of the proposed algorithm is theoretically analyzed. Finally, simulations are carried out to illustrate that the performance of the ASCKF algorithm is much more reliable than that of a standard square-root cubature Kalman filter.

Highlights

The accurate and reliable state estimation of nonlinear systems plays a crucial role in numerous practical engineering systems such as navigation, environment monitoring, intelligent manufacturing, and target tracking [1]–[5]
An increasing number of researchers have been interested in the state estimation of nonlinear systems, and several nonlinear filtering algorithms have been developed [6]–[8], including extended Kalman filter (EKF) algorithms [9]–[11], unscented Kalman filter (UKF) algorithms [12]–[14], and cubature Kalman filter (CKF) algorithms [15]–[17]
The proposed algorithm adaptively updates the parameters of the unknown noise, including the mean and covariance, by combining the maximum likelihood (ML) criterion and EM algorithm with the square-root cubature Kalman filter (SCKF) algorithm

Summary

INTRODUCTION

The accurate and reliable state estimation of nonlinear systems plays a crucial role in numerous practical engineering systems such as navigation, environment monitoring, intelligent manufacturing, and target tracking [1]–[5]. We found that there is very limited research that employs the ML criterion and EM algorithm with the CKF to estimate unknown noise. The proposed algorithm adaptively updates the parameters of the unknown noise, including the mean and covariance, by combining the ML criterion and EM algorithm with the square-root cubature Kalman filter (SCKF) algorithm. The estimation accuracy is improved based on the statistical characteristics of the unknown noise that can be obtained by the online estimation. The SCKF, as an improvement to the CKF, has shown promise in nonlinear systems and has been used for state estimation with unknown noise. When the statistical characteristics of noise are difficult to accurately obtain in engineering practice, the error of filtering will be increased, and the estimation accuracy will be seriously degraded.

M-STEP

SIMULATIONS

EXAMPLE 1

EXAMPLE 2 The state equation is expressed as

CONCLUSION