A robust filter and smoother-based expectation–maximization algorithm for bilinear systems with heavy-tailed noise

• Published in: Mechanical systems and signal processing Vol. 236; p. 112912
• Main Authors: Wang, Wenjie, Liu, Siyu, Jiang, Yonghua, Sun, Jianfeng, Xu, Wanxiu, Chen, Xiaohao, Dong, Zhilin, Jiao, Weidong
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2025
• Subjects: Bilinear system; Heavy-tailed noise; Parameter estimation; Robust filter; State estimation; Student’s t distribution; Bilinear system; Parameter estimation; Robust filter; State estimation; Student’s t distribution; Heavy-tailed noise
• ISSN: 0888-3270
• DOI: 10.1016/j.ymssp.2025.112912

This paper focuses on a specific type of nonlinear systems—bilinear systems and introduces a robust filter and smoother-based expectation–maximization (RFS-EM) algorithm that enables joint estimation of states and parameters in the presence of heavy-tailed noise. Specifically, to mitigate the impact of heavy-tailed noise, this study explores a combination method of robust filter and smoother based on Student’s t distribution, integrating it into an expectation–maximization framework. In the expectation step, forward and backward predictions of system states are performed using the robust filter and smoother. Following this, in the maximization step, system parameters are estimated through numerical optimization. The proposed RFS-EM achieves joint estimation of the states and parameters for bilinear systems. Finally, a numerical simulation and a DC motor simulation validate the effectiveness of the proposed algorithm.