Maximum Correntropy Generalized Conversion-Based Nonlinear Filtering

Nonlinear filtering methods have gained prominence in various applications, and one of the notable methods is the generalized conversion filter (GCF) based on deterministic sampling. The GCF offers an innovative method for converting measurements, exhibiting superior estimation performance when compared to several popular existing nonlinear estimators. However, a notable limitation of existing GCF is their reliance on the minimum mean square error (MMSE) criterion. While GCF excels in environments with Gaussian noise, their performance can significantly deteriorate in the presence of non-Gaussian noise, particularly when subjected to heavy-tailed impulse noise interference. To address this challenge and enhance the robustness of GCF against impulse noise, this article proposes a novel nonlinear filter known as the maximum correntropy GCF (MCGCF). Similar to GCF, the proposed filter also employs a general measurement conversion, wherein deterministic sampling is utilized to optimize the first and second moments of multidimensional transformations. To obtain a robust posterior estimate of the state and covariance matrices, the MCGCF employs a nonlinear regression method to derive state updates based on the maximum correntropy criterion (MCC). To validate the efficacy of the proposed MCGCF, two experiments are presented. These experiments illustrate the filter’s ability to deliver robust and accurate estimates, even in challenging scenarios with nonlinear systems and non-Gaussian noises.