Student’s t-Kernel-Based Maximum Correntropy Kalman Filter

Abstract

The state estimation problem is ubiquitous in many fields, and the common state estimation method is the Kalman filter. However, the Kalman filter is based on the mean square error criterion, which can only capture the second-order statistics of the noise and is sensitive to large outliers. In many areas of engineering, the noise may be non-Gaussian and outliers may arise naturally. Therefore, the performance of the Kalman filter may deteriorate significantly in non-Gaussian noise environments. To improve the accuracy of the state estimation in this case, a novel filter named Student’s t kernel-based maximum correntropy Kalman filter is proposed in this paper. In addition, considering that the fixed-point iteration method is used to solve the optimal estimated state in the filtering algorithm, the convergence of the algorithm is also analyzed. Finally, comparative simulations are conducted and the results demonstrate that with the proper parameters of the kernel function, the proposed filter outperforms the other conventional filters, such as the Kalman filter, Huber-based filter, and maximum correntropy Kalman filter.

A Redundant Measurement-Based Maximum Correntropy Extended Kalman Filter for the Noise Covariance Estimation in INS/GNSS Integration

“…Similar derivation also can be found in Ref. [17], in which a student's t kernel is adopted. The key idea is that if the kernel bandwidth is greater than a threshold value, then by Banach fixed-point Theorem, the fixed-point iteration algorithm will surely converge to a unique fixed point.…”

“…Although the kernel technique can provide higher robustness when the non-Gaussian noises exist. Unfortunately, if the noise encountered by the filter is timevarying and contains many impulsive elements or heavy-tailed properties, the performance of the MCEKF would not be as good as desired [17]. The limitations of MCEKF are given in the next subsection.…”

“…However, if the measurement noise or the process noise contains non-Gaussian components, the performance of the above filters would be severely degraded [17]. For example, the Middleton Class-A model, Middleton Class-B model, alpha-stable distribution model, and the mixture Gaussian model are frequently discussed non-Gaussian noises [18].…”

“…Therefore, based on the fact that the MMSE is no longer suitable for this type of noise, the corresponding robust adaptive filtering methods have been proposed to address the issue by introducing different metrics, such as the Huber-based algorithms [25]. However, these filters can achieve desirable results only under certain conditions [17]. The maximum correntropy Kalman filter (MCKF) can be employed to address non-Gaussian noise problems, which was inspired by the information learning theorem (ILT) [26,27].…”

An Improved Adaptive Iterative Extended Kalman Filter Based on Variational Bayesian

“…Numerous filters have been proposed to address the issue of heavy-tailed noise impacting system tracking. Notable among these are the robust variational Bayesian filter [18][19][20], Student's t-based filters (RSTFs) [21,22], Huber's M-estimation-based filters [23,24], and the maximum correlation entropy-based filters [25]. While these filters demonstrate enhanced tracking performance and effectively mitigate the negative impact of heavy-tailed noise, they face challenges in precise parameter selection and computational complexity.…”