This paper is concerned with parameter estimation of finite impulse response (FIR) systems with binary observations. Combining a suitable design of the time-varying thresholds, a kind of sign-error type unified algorithm with projection is investigated for either deterministic systems or stochastic systems. The convergence properties of the studied algorithm are established under bounded persistent excitations. Specifically, for the case without noise, the square convergence rate is proved to be close to O(1/k2) with respect to the time step k. For the case with bounded noises, the upper bound of the estimation error is obtained, which depends on the bound of the noises and the lower bound of the input persistent excitation condition. For the case with independent and identically distributed (i.i.d.) stochastic noises, the estimate is shown to converge to the true parameter in the sense of mean square and almost surely. Besides, the mean square convergence rate of the estimation error is of the order O(1/k). Numerical examples are supplied to demonstrate the theoretical results.
Publication:
Automatica, Volume 135: 109990, January 2022
Author:
Ying Wang
Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Email: wangying96@amss.ac.cn
Yanlong Zhao
Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Email: ylzhao@amss.ac.cn
Ji-Feng Zhang
Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Email: jif@iss.ac.cn
Jin Guo
The School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, PR China
Email: guojin@ustb.edu.cn
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