Combined Cubature Kalman and Smooth Variable Structure Filtering Based on Multi-Kernel Maximum Correntropy Criterion for the Fully Submerged Hydrofoil Craft

Abstract

This paper introduces a novel filter algorithm termed as an MKMC-CSVSF which combined square-root cubature Kalman (SR-CKF) and smooth variable structure filtering (SVSF) under multi-kernel maximum correntropy criterion (MKMC) for accurately estimating the state of the fully submerged hydrofoil craft (FSHC) under the influence of uncertainties and multivariate heavy-tailed non-Gaussian noises. By leveraging the precision of the SR-CKF and the robustness of the SVSF against system uncertainties, the MKMC-CSVSF integrates these two methods by introducing a time-varying smooth boundary layer along with multiple fading factors. Furthermore, the MKMC is introduced for the adjustment of kernel bandwidths across different channels to align with the specific noise characteristics of each channel. A fuzzy rule is devised to identify the appropriate kernel bandwidths to ensure filter accuracy without undue complexity. The precision and robustness of state estimation in the face of heavy-tailed non-Gaussian noises are improved by modifying the SR-CKF and the SVSF using a fixed-point approach based on the MKMC. The experimental results validate the efficacy of this algorithm.