Bias-compensation-based least-squares estimation with a forgetting factor for output error models with white noise

Abstract

In this paper, the bias-compensation-based recursive least-squares (LS) estimation algorithm with a forgetting factor is proposed for output error models. First, for the unknown white noise, the so-called weighted average variance is introduced. With this weighted average variance, a bias-compensation term is first formulated to achieve the bias-eliminated estimates of the system parameters. Then, the weighted average variance is estimated. Finally, the final estimation algorithm is obtained by combining the estimation of the weighted average variance and the recursive LS estimation algorithm with a forgetting factor. The effectiveness of the proposed identification algorithm is verified by a numerical example.

Keywords:

• output error models
• bias compensation
• recursive least-squares estimation
• forgetting factors

Acknowledgements

The authors are very grateful to the anonymous reviewers for their constructive comments, which have significantly improved the presentation of the paper.

Additional information

Funding

This paper was supported by the Project for Distinguished Young Scholars of the Basic Research Plan in Shenzhen City [Contract No. JCJ201110001]; the National Natural Science Foundation of China [grant number 61273094], [grant number 61321062], [grant number 61203125], [grant number 61333003]; the Specialised Research Fund for the Doctoral Program of Higher Education [grant number 20132302110053]; the Key Laboratory of Electronics Engineering, College of Heilongjiang Province (Heilongjiang University).

Notes on contributors

A.G. Wu

Ai-Guo Wu was born in Gong'an County, Hubei Province, P.R. China, on 20 September 1980. He received his BEng degree in automation in July 2002, MEng degree in navigation, guidance and control in July 2004 and PhD degree in control science and engineering in November 2008, all from Harbin Institute of Technology. In October 2008, he joined Harbin Institute of Technology Shenzhen Graduate School, where he is now a professor. Prof. Wu visited City University of Hong Kong from March 2009 to March 2011 as a research fellow. His research interests include descriptor systems, conjugate product of polynomials, system identification and robust control. Prof. Wu is a reviewer for American Mathematical Review and a member of the Editorial Board of theJournal of Control Science and Engineering. He was an outstanding reviewer for IEEE Transactions on Automatic Control. He received the National Excellent Doctoral Dissertation Award in 2011 from the Academic Degrees Committee of the State Council and the Ministry of Education of P.R. China. He was supported by the Program for New Century Excellent Talents in University in 2011. He is the author and co-author of over 50 SCI journal papers.

S. Chen

Shuang Chen was born in Benxi City, Liaoning Province, on 2 February 1987. She received her BEng degree in automation in 2007. Now, she is a graduate student majoring in control science and engineering in Harbin Institute of Technology, Shenzhen Graduate School. Now her main research interest is system identification.

D.L. Jia

Da-Ling Jia was born in Dengzhou City, Henan Province, on 27 April 1982. She received her BEng degree in automation from Harbin Institute of Technology in 2002 and MEng degree in 2005 in navigation, guidance and control from the Second Academy of China Aerospace Corporation. She is currently a senior engineer in China Academy of Launch Vehicle Technology (CALT). Now, her main research interests include navigation, attitude control and system identification.