On the computation of the structured total least squares estimator
On the computation of the structured total least squares estimator
A class of structured total least squares problems is considered, in which the extended data matrix is partitioned into blocks and each of the blocks is (block) Toeplitz/Hankel structured, unstructured, or noise free. We describe the implementation of two types of numerical solution methods for this problem: i) standard local optimization methods in combination with efficient evaluation of the cost function and its gradient, and ii) an iterative procedure proposed originally for the element-wise weighted total least squares problem. The computational efficiency of the proposed methods is compared with this of alternative methods. Application of the structured total least squares problem for system identification and model reduction is described and illustrated with numerical examples.
parameter estimation, total least squares, structured total least squares, system identification, Hankel low rank approximation, model reduction.
591-608,
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678
Kukush, A.
9cf76e13-c463-47c3-9467-0ae6b04df4ef
2004
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678
Kukush, A.
9cf76e13-c463-47c3-9467-0ae6b04df4ef
Markovsky, I., Van Huffel, S. and Kukush, A.
(2004)
On the computation of the structured total least squares estimator.
Numerical Linear Algebra with Applications, 11, .
Abstract
A class of structured total least squares problems is considered, in which the extended data matrix is partitioned into blocks and each of the blocks is (block) Toeplitz/Hankel structured, unstructured, or noise free. We describe the implementation of two types of numerical solution methods for this problem: i) standard local optimization methods in combination with efficient evaluation of the cost function and its gradient, and ii) an iterative procedure proposed originally for the element-wise weighted total least squares problem. The computational efficiency of the proposed methods is compared with this of alternative methods. Application of the structured total least squares problem for system identification and model reduction is described and illustrated with numerical examples.
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Published date: 2004
Keywords:
parameter estimation, total least squares, structured total least squares, system identification, Hankel low rank approximation, model reduction.
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Southampton Wireless Group
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Local EPrints ID: 263297
URI: http://eprints.soton.ac.uk/id/eprint/263297
PURE UUID: 218bc03c-022a-4ae6-9fe0-5d402da2d6b8
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Date deposited: 06 Jan 2007
Last modified: 14 Mar 2024 07:28
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Author:
I. Markovsky
Author:
S. Van Huffel
Author:
A. Kukush
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