Data filtering-based parameter and state estimation algorithms for state-space systems disturbed by coloured noises

ABSTRACT

In this paper, the combined parameter and state estimation issues of state-space systems are considered, and the process noises and observation noises are supposed to be coloured noises. By utilising the data filtering technique, we transform the original state-space system into the filtered system for eliminating the interference of the coloured noise in the state equation, and then we derive a filtering-based extended stochastic gradient (F-ESG) algorithm to estimate the system parameters. For estimating the unmeasurable states, we derive a new state estimator by using the preceding parameter estimates to take the place of the unknown system parameters in the Kalman filter. Furthermore, we propose a filtering-based multi-innovation extended stochastic gradient (F-MI-ESG) algorithm to achieve the higher parameter estimation accuracy. Finally, we provide two simulation examples to test and compare the performance of the proposed algorithms. The simulation results indicate that the F-ESG algorithm and the F-MI-ESG algorithm are effective for parameter estimation, and that the F-MI-ESG algorithm is able to achieve more accurate parameter estimates than the F-ESG algorithm.

KEYWORDS:

• State-space system
• parameter estimation
• data filtering technique
• gradient search
• multi-innovation identification

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61873111] and the 111 Project [grant number B12018].

Notes on contributors

Ting Cui

Ting Cui was born in Taiyuan (Shanxi Province, China) in 1994. She received her B.Sc. degree from Jiangnan University (Wuxi, China) in 2017, and now is a Ph.D. student in the School of Internet of Things Engineering, Jiangnan University (Wuxi, China). Her interests include system modeling, system identification and process control.

Feng Ding

Feng Ding received his B.Sc. degree from the Hubei University of Technology (Wuhan, China) in 1984, and his M.Sc. and Ph.D. degrees both from the Tsinghua University in 1991 and 1994, respectively. He has been a professor in the School of Internet of Things Engineering at the Jiangnan University (Wuxi, China) since 2004. His current research interests include model identification and adaptive control. He authored five books on System Identification.

Ahmed Alsaedi

Ahmed Alsaedi obtained his Ph.D. degree from Swansea University (UK) in 2002. He has a broad experience of research in applied mathematics. His fields of interest include dynamical systems, nonlinear analysis involving ordinary differential equations, fractional differential equations, boundary value problems, mathematical modeling, biomathematics, Newtonian and Non-Newtonian fluid mechanics. He served as the chairman of the mathematics department at KAU and presently he is serving as a director of the research program at KAU. Under his great leadership, this program is running quite successfully and it has attracted a large number of highly rated researchers and distinguished professors from all over the world. He is also the head of NAAM international research group at KAU.

Tasawar Hayat

Tasawar Hayat was born in Khanewal, Punjab. Distinguished National Professor and Chairperson of Mathematics Department at Quaid-I-Azam University, he is renowned worldwide for his seminal, diversified and fundamental contributions in models relevant to physiological systems, control engineering. He has an honor of being fellow of Pakistan Academy of Sciences, Third World Academy of Sciences (TWAS) and Islamic World Academy of Sciences in the Mathematical Sciences.