Least-squares estimation of input/output models for distributed linear systems in the presence of noise

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• 作者：Gibson ; J.S. ; Lee ; G.H. ; et. al.
• 关键词：Least-squares parameter estimation ; Noisy data ; Distributed systems
• 刊名：Automatica
• 出版年：2000
• 出版时间：October, 2000
• 年：2000
• 卷：36
• 期：10
• 页码：1427-1442
• 全文大小：330 K

文摘

This paper addresses least-squares estimation of parameters in digital input/output models of linear time-invariant distributed systems in the presence of white process and sensor noise. The systems of interest have state-space realizations in Hilbert spaces. Both finite-dimensional and infinite-dimensional input/output models are considered. The paper derives a number of new results for recursive least-squares estimation and filtering. The main results characterize the asymptotic values to which parameter estimates converge with increasing amounts of data. The most important result is an equivalence between least-squares parameter estimation on an infinite interval (i.e., with infinitely long data sequences) and linear-quadratic optimal control on a finite interval. Numerical results are presented for a sampled-data version of a wave equation.