Multi-Model Minimum Error Entropy Recursive Three-Step Filter

This paper investigates state estimation for strongly nonlinear systems with unknown inputs under non-Gaussian heavy-tailed impulsive noise. Conventional recursive three-step filters (RTSF) based on the minimum-variance criterion are sensitive to outliers, while a single local linearization is often inadequate for strongly nonlinear dynamics. To overcome these limitations, a multi-model minimum error entropy recursive three-step filter (MMMEERTSF) is proposed. The minimum error entropy criterion is embedded into the RTSF framework to enhance robustness against abnormal disturbances, and iterative reweighted solutions are developed for unknown-input estimation and state correction by combining residual whitening with entropy-based optimization. Meanwhile, multiple local linear submodels are constructed to approximate the nonlinear system, and compatibility-based posterior fusion is employed to obtain the final estimate. The proposed method shows improved robustness and competitive estimation accuracy under non-Gaussian mixture and impulsive noise, especially in the nonlinear multi-model case.