Parameter estimation algorithms of linear systems with time-delays based on the frequency responses and harmonic balances under the multi-frequency sinusoidal signal excitation

• Published in: Signal processing Vol. 181; p. 107904
• Main Authors: Ni, Jiayao, Zhang, Yanliang, Ding, Feng, Zhan, Xi-Sheng, Hayat, Tasawar
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2021
• Subjects: Frequency characteristics; Frequency response; Harmonic balance; Multi-innovation theory; Sinusoidal signal; Time-delay system; Multi-innovation theory; Frequency response; Sinusoidal signal; Time-delay system; Frequency characteristics; Harmonic balance
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2020.107904

•Study the parameter and time-delay estimation algorithm for linear systems.•Present a two-stage stochastic gradient and gradient-based iterative algorithm.•Present a multi-innovation stochastic gradient algorithm to improve the accuracy. In this paper, we study the parameter estimation problem of a class of linear time-delay systems. Based on the frequency responses and harmonic balance methods and by means of the gradient search, a two-stage stochastic gradient and gradient-based iterative algorithm is developed by using the collected data under the sinusoidal excitation. To improve the estimation accuracy, a two-stage multi-innovation stochastic gradient and gradient-based iterative algorithm is presented. Two simulation examples are provided to test the proposed algorithms.