Multistage parameter estimation algorithms for identification of bilinear systems

In this paper, two methods for parameter estimation of bilinear state-space systems with colored noise, which are expressed by ARMA model, are proposed. Using the hierarchical identification principle and gradient method, to reduce the computational cost, both the four-stage recursive least squares...

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Bibliographic Details
Published in:Nonlinear dynamics Vol. 110; no. 3; pp. 2635 - 2655
Main Authors: Shahriari, Fatemeh, Arefi, Mohammad Mehdi, Luo, Hao, Yin, Shen
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.11.2022
Springer Nature B.V
Subjects:
Accuracy
Algorithms
Automotive Engineering
Classical Mechanics
Control
Convergence
Decomposition
Design
Dynamical Systems
Engineering
Error reduction
Identification
Iterative methods
Kalman filters
Least squares
Mechanical Engineering
Methods
Original Paper
Parameter estimation
Parameter identification
State estimation
State observers
Vibration
Gradient search
Parameter estimation
Bilinear systems
Hierarchical identification
ISSN:0924-090X, 1573-269X
Online Access:Get full text
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Summary:In this paper, two methods for parameter estimation of bilinear state-space systems with colored noise, which are expressed by ARMA model, are proposed. Using the hierarchical identification principle and gradient method, to reduce the computational cost, both the four-stage recursive least squares algorithm and the four-stage stochastic gradient algorithm are exploited by which parameter estimation error is reduced and the speed of convergence of parameters is increased. In addition, a bilinear state observer for state estimation is designed to make use of the estimated states in the four-stage recursive least squares and the four-stage stochastic gradient algorithms. Finally, a numerical example and a practical example are provided to indicate the superiority of the proposed methods. The results show that due to the data length increase, the estimation error of the parameters is reduced. Furthermore, the estimated parameters converge to the actual values in a short time.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-022-07749-0