Maximum likelihood based identification methods for rational models

ABSTRACT

In a rational model, some terms of the information vector are correlated with the noise, which makes the traditional least squares based iterative algorithms biased. In order to overcome this shortcoming, this paper develops two recursive algorithms for estimating the rational model parameters. These two algorithms, based on the maximum likelihood principle, have three integrated key features: (1) to establish two unbiased maximum likelihood recursive algorithms, (2) to develop a maximum likelihood recursive least squares (ML-RLS) algorithm to decrease the computational efforts, (3) to update the parameter estimates by the ML-RLS based particle swarm optimisation (ML-RLS-PSO) algorithm when the noise-to-output ratio is large. Comparative studies demonstrate that (1) the ML-RLS algorithm is only valid for rational models when the noise-to-output ratio is small, (2) the ML-RLS-PSO algorithm is effective for rational models with random noise-to-output ratio, but at the cost of heavy computational efforts. Furthermore, the simulations provide cases for potential expansion and applications of the proposed algorithms.

KEYWORDS:

• Parameter estimation
• rational model
• maximum likelihood method
• PSO algorithm
• recursive least squares algorithm

Acknowledgements

The authors would like to express their gratitude to the Associate Editor and the anonymous reviewers for their constructive comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Feng Ding  http://orcid.org/0000-0002-2721-2025

Additional information

Funding

This work was supported by the Natural Science Foundation for Colleges and Universities in Jiangsu Province (no. 16KJB120006), Qinglan Project of Jiangsu Province, Fundamental Research Funds for the Central Universities (JUSRP11833) and National First-Class Discipline Program of Light Industry Technology and Engineering (LITE2018-26).

Notes on contributors

Jing Chen

Jing Chen received his B.Sc. degree in the School of Mathematical Science and M.Sc. degree in the School of Information Engineering from Yangzhou University (Yanghzou, China) in 2003 and 2006, respectively, and received his Ph.D. degree in the School of Internet of Things Engineering, Jiangnan University (Wuxi, China) in 2013. He is currently an associate professor in the School of Science, Jiangnan University (Wuxi, China). He is a Colleges and Universities “BlueProject” Middle-Aged Academic Leader (Jiangsu, China). His research interests include Processing Control and system identification.

Feng Ding

Feng Ding was born in Guangshui, Hubei Province, China. He received the B.Sc. degree from the Hubei University of Technology (Wuhan, China) in 1984, and the M.Sc. and Ph.D. degrees in automatic controlboth from the Department of Automation, Tsinghua University, Beijing, in 1991 and 1994, respectively. He has been a Professor in the School of Internet of Things Engineering, Jiangnan University, Wuxi, China since 2004. He is a Colleges and Universities “BlueProject” Middle-Aged Academic Leader (Jiangsu, China). His current research interests include model identification and adaptive control. He authored four books on System Identification.

Quanmin Zhu

Quanmin Zhu is Professor in control systems at the Department of Engineering Design and Mathematics, University of the West of England, Bristol, UK. He obtained his MSc in Harbin Institute of Technology, China in 1983 and PhD in Faculty of Engineering, University of Warwick, UK in 1989. His main research interest is in the area of nonlinear system modelling, identification, and control. His other research interest is in investigating electrodynamics of acupuncture points and sensory stimulation effects in human body, modelling of human meridian systems, and building up electro-acupuncture instruments. He has published over 200 papers on these topics, edited five Springer books and one book for the other publisher, and provided consultancy to various industries. Currently Professor Zhu is acting as Editor of International Journal of Modelling, Identification and Control, Editor of International Journal of Computer Applications in Technology, Member of Editorial Committee of Chinese Journal of Scientific Instrument, and editor of Elsevier book series of Emerging Methodologies and Applications in Modelling, Identification and Control. He is the founder and president of series annual International Conference on Modelling, Identification and Control.

Yanjun Liu

Yanjun Liu received the B.Sc. degree from Jiangsu  University of Technology (Changzhou, China) in 2003, the M.Sc. degree and the Ph.D. degree from Jiangnan University (Wuxi, China) in 2009 and 2012, respectively. She is currently an associate professor in the School of Internet of Things Engineering, Jiangnan University. Her research interests are system identification and parameter estimation.