Multi-Model Minimum Error Entropy Recursive Three-Step Filter
Xiaoliang Feng1, Jiawei Zhang1
1School of Electrical and Energy Engineering, Shanghai Dianji University, Shanghai 201306, China.
Entropy (Basel, Switzerland)
|July 28, 2026
Summary
This study introduces a robust state estimation filter for nonlinear systems with unknown inputs and heavy-tailed noise. The novel multi-model minimum error entropy recursive three-step filter (MMMEERTSF) enhances accuracy and resilience against outliers.
Area of Science:
- Control Systems Engineering
- Signal Processing
- Nonlinear Dynamics
Background:
- State estimation for nonlinear systems is challenging due to strong nonlinearities and non-Gaussian noise.
- Conventional filters like recursive three-step filters (RTSF) are sensitive to outliers and struggle with significant nonlinearities.
- Existing methods often fail under heavy-tailed impulsive noise conditions.
Purpose of the Study:
- To develop a robust state estimation method for strongly nonlinear systems with unknown inputs under non-Gaussian heavy-tailed impulsive noise.
- To enhance the resilience of recursive three-step filters (RTSF) against outliers and improve accuracy in nonlinear dynamics.
- To address the limitations of conventional minimum-variance criteria and single local linearization approaches.
Main Methods:
- A multi-model minimum error entropy recursive three-step filter (MMMEERTSF) is proposed.
- The minimum error entropy criterion is integrated into the RTSF framework for outlier robustness.
- Iterative reweighted solutions combining residual whitening and entropy optimization are used for unknown-input estimation and state correction.
- Multiple local linear submodels approximate the nonlinear system, with compatibility-based posterior fusion for the final estimate.
Main Results:
- The proposed MMMEERTSF demonstrates improved robustness against non-Gaussian mixture and impulsive noise.
- The method achieves competitive estimation accuracy compared to conventional approaches.
- Enhanced performance is particularly noted in nonlinear multi-model scenarios.
Conclusions:
- The MMMEERTSF offers a robust and accurate solution for state estimation in challenging nonlinear systems with unknown inputs and impulsive noise.
- The integration of minimum error entropy and multi-model strategies effectively handles non-Gaussian disturbances.
- This approach provides a significant advancement for state estimation under adverse noise conditions.
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