Maximum Correntropy Square-Root Cubature Kalman Filter for Non-Gaussian Measurement Noise

Abstract

Cubature Kalman filter (CKF) is widely used for non-linear state estimation under Gaussian noise. However, the estimation performance may degrade greatly in presence of heavy-tailed measurement noise. Recently, maximum correntropy square-root cubature Kalman filter (MCSCKF) has been proposed to enhance the robustness against measurement outliers. As is generally known, the square-root algorithms have the benefit of low computational complexity and guaranteed positive semi-definiteness of the state covariances. Therefore, MCSCKF not only possesses the advantages of square-root cubature Kalman filter (SCKF), but also is robust against the heavy-tailed measurement noise. Nevertheless, MCSCKF is prone to the numerical problems. In this paper, we propose a new maximum correntropy square-root cubature Kalman filter (NMCSCKF) based on a cost function which is obtained by a combination of weighted least squares (WLS) to handle the Gaussian process noise and maximum correntropy criterion (MCC) to handle the heavy-tailed measurement noise. Compared to MCSCKF, the proposed method is more time-efficient and most importantly, it avoids the numerical problem. A univariate non-stationary growth model and a multi-rate vision/IMU integrated attitude measurement model are used to demonstrate the superior performance of the proposed method.