Hierarchical multi-innovation stochastic gradient identification algorithm for estimating a bilinear state-space model with moving average noise

Gu, Ya; Dai, Wei; Zhu, Quanmin; Nouri, Hassan

Abstract

This paper considers the combined parameter and state estimation problem of a bilinear state space system with moving average noise. There are product terms of state variables and control variables in bilinear systems, which brings difficulties to parameter and state estimation. By designing a bilinear state estimator based on Kalman filter and using input–output data to estimate the state, a hierarchical multi-innovation stochastic gradient (i.e., H-MISG) algorithm based on the state estimator is proposed to jointly estimate unknown states and parameters. In addition, compared with the hierarchical stochastic gradient algorithm, H-MISG algorithm introduces the innovation length parameter, makes full use of the system input and output data information, and improves the accuracy of parameter estimation. Numerical simulation examples verify the effectiveness of the proposed algorithm.

• Journal Article Type: Article
• Acceptance Date: Aug 22, 2022
• Online Publication Date: Aug 31, 2022
• Publication Date: Mar 1, 2023
• Deposit Date: Oct 4, 2022
• Publicly Available Date: Mar 1, 2024
• Journal: Journal of Computational and Applied Mathematics
• Print ISSN: 0377-0427
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 420
• Pages: 114794
• DOI: https://doi.org/10.1016/j.cam.2022.114794
• Keywords: Bilinear system, Multi-innovation identification, Kalman filtering, Parameter estimation, State estimation
• Public URL: https://uwe-repository.worktribe.com/output/10018898
• Publisher URL: https://www.sciencedirect.com/science/article/abs/pii/S0377042722004046?via%3Dihub