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

This paper addresses least-squares estimation of parameters in digital inpu t/output models of linear time-invariant distributed systems in the presenc e of white process and sensor noise. The systems of interest have state-spa ce realizations in Hilbert spaces. Both finite-dimensional and infinite-dim ensional 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 con verge with increasing amounts of data. The most important result is an equi valence between least-squares parameter estimation on an infinite interval (i.e., with infinitely long data sequences) and linear-quadratic optimal co ntrol on a finite interval. Numerical results are presented for a sampled-d ata version of a wave equation. (C) 2000 Elsevier Science Ltd. All rights r eserved.