Gaussian-Cauchy Mixture Kernel Function Based Maximum Correntropy Criterion Kalman Filter for Linear Non-Gaussian Systems

This paper proposes a Gaussian-Cauchy mixture maximum correntropy criterion Kalman filter algorithm (GCM_MCCKF) for robust state estimation in linear systems under non-Gaussian noise, particularly heavy-tailed noise. The performance of the MCCKF depends on the choice of kernel type and its associated kernel parameters. First, in terms of kernel type, it affects the sensitivity of the filter to noise and outliers. To overcome the limitations of a single zero-mean Gaussian kernel function in MCC, this paper proposes and derives the Gaussian-Cauchy mixture kernel function-based MCCKF. Some important properties of the Gaussian-Cauchy mixture correntropy are also studied. Second, in terms of kernel parameters, this paper draws on established techniques while incorporating innovative elements, heuristically proposes a suitable adaptive update scheme for kernel size to overcome the limitations of fixed kernel size in practical applications. Finally, the target tracking simulation example is used to verify that the proposed GCM_MCCKF algorithm can handle heterogeneous and complex data more flexibly and stably under the proposed kernel size adaptive update scheme, and obtain better filtering performance than the traditional KF filter, variational Bayesian filtering (VB), particle filter (PF), minimum error entropy KF (MEE_KF), single Gaussian kernel MCCKF (G_MCCKF) and double-Gaussian mixture MCCKF (DGM_MCCKF).