DCM_MCCKF: A non-Gaussian state estimator with adaptive kernel size based on CS divergence

Abstract

In practical industrial system models, noise is better characterized by heavy-tailed non-Gaussian distributions. For state estimation in systems with heavy-tailed non-Gaussian noise, the maximum correntropy criterion (MCC) based on information theoretic learning (ITL) is widely adopted, achieving good filtering performance. The performance of MCC-based filtering depends on the selection of the kernel function and its parameters. To overcome the sensitivity of the Gaussian kernel to its parameters and the limitation of a single kernel function in comprehensively reflecting the characteristics of complex heterogeneous data, a double-Cauchy mixture-based MCC Kalman Filtering (DCM_MCCKF) algorithm is proposed. This selection uses a mixture of two Cauchy kernel functions, using their heavy-tailed properties to better handle large errors and reduce sensitivity to kernel size variations. As a result, it improves the robustness and flexibility of MCC-based filtering. The kernel size should adapt to changes in signal distribution. To address the limitation of fixed kernel size, an adaptive kernel size update rule is designed by comprehensively considering system models, accessible measurements, CS divergence between noise distributions, and covariance propagation. Simulation examples of target tracking validate that the proposed DCM_MCCKF algorithm, under the adaptive kernel size updating rule, effectively handles complex data and achieves superior filtering performance in heavy-tailed non-Gaussian noise scenarios. This algorithm outperforms traditional Kalman filters (KF) based on the mean square error (MSE) criterion, Gaussian sum filtering (GSF), particle filtering (PF), and Maximum Correntropy Criterion Kalman filters (MCCKF) with a single Gaussian kernel (G_MCCKF), a double-Gaussian mixture kernel (DGM_MCCKF), and a Gaussian-Cauchy mixture kernel (GCM_MCCKF). Consequently, the DCM_MCCKF algorithm significantly enhances the applicability and robustness of MCC-based filtering methods.