Gaussian-Kernel-Based Maximum Correntropy Kalman Filter With Adaptive Kernel Scale Selection

Dynamic systems often encounter disturbances like sensor outliers, which violate the Gaussian noise assumption in traditional Kalman filters (KFs). While maximum correntropy KFs (MCKFs) address this issue by utilizing higher order statistical information, their performance critically depends on the manual selection of a kernel scale parameter. Existing methods with fixed or empirically adjusted kernel scales struggle to handle disturbances of varying intensities, limiting practical applications. This article presents a novel adaptive MCKF framework. The key contributions are as follows: 1) Adaptive Kernel Scale Optimization: The kernel scale is modeled as a probabilistic variable, and variational Bayesian inference is employed to jointly estimate the system state, enabling automatic kernel scale optimization during the recursive process. 2) Theoretical Analysis and Extension: The computational complexity of the proposed algorithm is analyzed in the context of linear systems, and its theoretical connection to traditional correlation entropy filters is established. Furthermore, the method is extended to nonlinear systems. 3) Performance Enhancement: Experimental evaluations on typical single-target tracking task and complex nonlinear scenario demonstrate that the proposed approach outperforms existing methods. Under various types of noise interference, the average position estimation error is reduced by 40%–60%, highlighting its superior adaptability and robustness. In addition, the algorithm is successfully applied to real-world battery state-of-charge (SOC) estimation in Internet of Things (IoT) scenarios, demonstrating its practical value in embedded energy management systems.