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. INDEX TERMS Square-root cubature Kalman filter, maximum correntropy criterion, vision/IMU integrated measurement.

Improved maximum correntropy cubature Kalman and information filters with application to target tracking under non‐Gaussian noise

“…where a and b denote the adjustment weights, 30,35 and the || ⋅ || 2 x = (⋅) T x(⋅) stands for the square of x-weighted Mahalanobis distance. Under the Gaussian kernel, the Mahalanobis distance can be expressed as…”

“…,then according to (32), Kk = K k is obtained, and Equation ( 39) is equal to Equation (30). Next, we consider the P k .…”

“…Lots of simulation examples show that these MCC‐based nonlinear filters can achieve better performance than the Huber's robust statistics 26–28 . However, the classical MCEKF and MCCKF and their corresponding filters 29,30 usually face numerical problems when the measurement values have some abnormally large noises, because these algorithms need to calculate the inverse of the matrices which are approaching zero. In addition, due to the constant weights obtained through the three‐degree cubature rule and differential operation, the classical MCCIF does not converge to the standard CIF, and its estimation performance is also declined 31 …”

Signal Detection for GSTFIM Systems with Carrier Frequency Offset

“…Under non-Gaussian noise, the calculation of the mean and variance of will be inaccurate, resulting in the inaccurate calculation of the subsequent posterior probability. In that case, we could substitute the MMSE criterion in Step 4 by the maximum correntropy criterion [ 26 ] to mitigate the inaccuracies. The correntropy between , with joint distribution is defined as where is the expectation operator and denotes a shift-invariant Mercer kernel, and where and represents the kernel bandwidth.…”

A novel robust interacting multiple model filter for manoeuvering target tracking

“…At the same time, the research of information theoretical learning (ITL) has been received widespread attention, and the correntropy of ITL theory has also made significant progress [11]. The maximum correntropy (MC) KF is recently proposed to deal with non-Gaussian noise in dynamic systems [12][13][14]. The existing filters based on maximum entropy mainly solve non-Gaussian noise, but do not consider the adaptability of target tracking.…”