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Bayesian Correntropy-Based State Estimation through Sequential Monte Carlo Method
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DOI：10.1016/j.dsp.2026.106209.png)
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Abstract
En 中文
Correntropy has emerged as a powerful similarity measure for robust signal processing, particularly under non-Gaussian noise scenarios. Existing correntropy-based filters typically incorporate the correntropy into minimum mean square error (MMSE)-derived estimators in order to improve robustness. In contrast, this work revisits the Bayesian estimation objective itself and introduces, for the first time, a Bayesian correntropy-based estimation criterion formulated directly with respect to the posterior distribution. This reformulation fundamentally changes the estimator structure: instead of modifying an MMSE solution, the proposed method derives a new estimator whose optimality is defined through correntropy itself. As a consequence, the resulting estimator is fundamentally non-MMSE and cannot be interpreted as a robustified MMSE solution. From this criterion, a novel Bayesian correntropy estimator is derived in fixed-point form. To implement this estimator in nonlinear and non-Gaussian state-space models, we propose an iterative maximum correntropy sequential Monte Carlo filtering (IMCSMCF) algorithm, which combines particle-based posterior approximation with iterative fixed-point refinement. The proposed algorithm provides a principled particle-based implementation of the Bayesian correntropy estimator, enabling robust nonlinear filtering without relying on Gaussian posterior approximations or local linearization. A rigorous convergence analysis of the proposed iterative estimator is also developed. Specifically, we derive sufficient conditions under which the fixed-point mapping becomes contractive, thereby guaranteeing existence, uniqueness, and convergence of the estimator. We establish both conservative and sharper bounds for the contraction constant and provide geometric interpretations based on particle spread. These results yield practical guidelines for selecting the correntropy kernel bandwidth. Monte Carlo simulations on a nonlinear system with Gaussian-mixture process and measurement noises demonstrate the effectiveness of the proposed framework. In moderate heavy-tailed noise conditions, IMCSMCF achieves a substantially lower estimation error than the standard particle filter, while requiring only few fixed-point iterations on average. Under severe impulsive noise, the proposed method also outperforms representative robust filters. Taken together, these results indicate that the proposed Bayesian correntropy formulation, together with the IMCSMCF algorithm and its convergence guarantees, yields a principled and robust alternative to conventional MMSE-based nonlinear filtering approaches.
Keywords:
Bayesian estimation
Correntropy
Sequential Monte Carlo
Nonlinear filtering
Robust state estimation
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