Robust Heterogeneous Multi-Kernel Maximum Correntropy Unscented Kalman Filter for Nonlinear Control Systems Under Non-Gaussian Noises

Abstract

While multikernel correntropy, as a powerful local similarity measure, has demonstrated superior robustness against non-Gaussian noise and outliers, existing approaches are limited by their reliance on homogeneous kernels and suboptimal treatment of free coefficients. To address this gap, this article introduces the concept of heterogeneous multikernel correntropy (HMKC), which employs a mixture of two Gaussian-Versoria functions with flexible, nonzero mean values as its kernel. Building on this criterion, we propose a unified unscented Kalman filter (UKF) framework, the robust heterogeneous multikernel maximum correntropy UKF (R-HMKMC-UKF), designed to enhance both estimation performance and numerical stability, thereby providing reliable state estimates for state-feedback control. The framework incorporates an enhanced particle swarm optimization algorithm to calculate and select free coefficients automatically. Simultaneously, to enhance numerical stability, a critical requirement for reliable implementation, we incorporate Moore–Penrose pseudoinversion and hyperbolic QR decomposition, which effectively address ill-conditioned matrix inversions and prevent loss of positive definiteness in covariance matrices. Finally, we validate the excellent accuracy and numerical stability of the proposed R-HMKMC-UKF in two challenging applications: IEEE 30-bus power system state estimation and land vehicle navigation, under multimodal noise and severe measurement outliers.