Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems

• Published in: Journal of the Franklin Institute Vol. 357; no. 8; pp. 5019 - 5032
• Main Authors: Ji, Yan, Jiang, Xiaokun, Wan, Lijuan
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.05.2020; Elsevier Science Ltd
• Subjects: Algorithms; Estimating techniques; Hierarchical identification principle; Impulse response; Innovations; Least squares; Mathematical models; Parameter estimation; Parameter identification; Parameterization; Recursive identification; System effectiveness; Recursive identification; Parameter estimation; Hierarchical identification principle; Least squares
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2020.03.027

This paper considers the parameter estimation problems of two-input single-output Hammerstein finite impulse response systems. A hierarchical least squares algorithm is proposed for improving the computational efficiency through combining the hierarchical identification principle and the identification model decomposition, and a multi-innovation least squares algorithm is proposed for enhancing the parameter estimation accuracy based on the multi-innovation identification theory. The key is to derive two sub-identification models, each of which contains a set of merged parameter vectors. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the over-parametrization identification method, and can be easily extended to multi-input multi-output systems. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.