Cauchy–Gaussian maximum mixture correntropy Kalman filter with component-by-component construction

The Kalman filter (KF) systematically optimizes the quasi-Monte Carlo (QMC) sampling points by employing a component-by-component (CBC) construction principle tailored to specific integration dimensions and accuracy requirements. This optimization enhances the approximation accuracy of Gaussian-weighted multidimensional integrals (GMIs) within the context of the KF. However, the KF based on CBC sampling points uses the minimum mean square error (MMSE) criterion, which can lead to significant estimation bias in the presence of non-Gaussian noises. To address this issue, this paper first proposes a novel Cauchy–Gaussian maximum mixture correntropy Kalman filter with component-by-component construction (CGMCKF-CBC) by the designed novel Cauchy–Gaussian maximum mixture correntropy (CGMC). Unlike the traditional maximum mixture correntropy criterion (MMCC), the CGMC uses the mixture of Cauchy kernel and Gaussian kernel as the cost function, and updates the posteriori estimates by the form of fixed-point iteration. Next, to further address the parameters selection issue existing in CGMCKF-CBC, an adaptive optimization strategy is proposed to determine appropriate parameters, resulting a variable CGMCKF-CBC (VCGMCKF-CBC). Then, the convergence analysis and complexity evaluation of CGMCKF-CBC are also conducted. Finally, two simulation examples are conducted in non-Gaussian noises environments to validate the excellent filtering accuracy and robustness of CGMCKF-CBC and VCGMCKF-CBC.