Maximum Correntropy Unscented Kalman Filter With Unsupervised Adaptive Kernel Scale Selection

Dynamic systems in practice are often nonlinear and subject to complex disturbances such as sensor outliers, which invalidate the Gaussian noise assumptions underlying conventional Kalman filters. To address the limitations of conventional Kalman filters under such conditions, recent studies have explored nonlinear filters based on the maximum correntropy criterion (MCC), which exploit both second-order and higher-order moments of the innovation for enhanced robustness. However, their performance is highly sensitive to the choice of kernel scale, and existing strategies—whether fixed offline or empirically adjusted—fail to adapt to unknown disturbances of varying intensities. This paper proposes a novel unsupervised adaptive maximum correntropy unscented Kalman filter (AMCUKF), which introduces three major contributions: (1) Online Kernel Scale Adaptation—the kernel scale is modeled as a latent random variable governed by an inverse Gamma distribution, and variational Bayesian inference is applied to jointly estimate the system state and kernel scale in a recursive manner; (2) Theoretical Consistency and Closed-Form Solutions—the algorithm maintains consistency with traditional MCUKF but achieves dynamic adaptability through the conjugacy of Gaussian and inverse Gamma priors, enabling efficient closed-form updates; and (3) Validated Performance under Non-Gaussian Noise—comprehensive tests on three representative scenarios, including nonlinear numerical systems with stationary/non-stationary t-distributed and Cauchy measurement noise, a single-target tracking task, and real-world battery state-of-charge (SoC) estimation using the public LG 18650 HG2 dataset. Compared with UKF, EMCUKF and FMCUKF, the proposed AMCUKF achieves about 20–60% lower RMSE and 30–70% lower worst-case error across heavy-tailed noise simulations, while maintaining comparable computational cost and convergence within 1–3 iterations. In the real-world SoC estimation task, it further reduces the maximum estimation error from over 7% to below 1%, demonstrating strong practical robustness.