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The element-wise weighted total least squares problem

The element-wise weighted total least squares problem
The element-wise weighted total least squares problem
A new technique for parameter estimation is considered in a linear measurement error model AX approx B, A = A0 + tilde A, B = B0 + tilde B, with row-wise independent and non-identically distributed measurement errors tilde A, tilde B. The total least squares method yields an inconsistent estimate of the parameter X in this case. We formulate a modified total least squares problem, called element-wise weighted total least squares, which provides a consistent estimator, and propose two iterative algorithms for its solution. A local convergence and the rate of convergence of the algorithms is discussed. As a computationally cheap initial approximation we use the generalized total least squares estimate.
Total least squares, Multivariate errors-in-variables model, Unequally sized errors, Non-convex optimization, Re-weighted least-squares
0167-9473
181 -209
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Rastello, M.
407e439c-b0f2-4dd0-9dd4-bbb9154b1fe1
Premoli, P.
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Van Huffel, S.
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Barlow, J.
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Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Rastello, M.
407e439c-b0f2-4dd0-9dd4-bbb9154b1fe1
Premoli, P.
29163217-1ecc-4640-b8a2-4cea3b53e363
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678
Barlow, J.
a79fb2a6-04e7-400e-a67e-8625743bef60

Markovsky, I., Rastello, M., Premoli, P. and Van Huffel, S. , Barlow, J. (ed.) (2006) The element-wise weighted total least squares problem. Computational Statistics and Data Analysis, 51 (1), 181 -209.

Record type: Article

Abstract

A new technique for parameter estimation is considered in a linear measurement error model AX approx B, A = A0 + tilde A, B = B0 + tilde B, with row-wise independent and non-identically distributed measurement errors tilde A, tilde B. The total least squares method yields an inconsistent estimate of the parameter X in this case. We formulate a modified total least squares problem, called element-wise weighted total least squares, which provides a consistent estimator, and propose two iterative algorithms for its solution. A local convergence and the rate of convergence of the algorithms is discussed. As a computationally cheap initial approximation we use the generalized total least squares estimate.

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Published date: January 2006
Keywords: Total least squares, Multivariate errors-in-variables model, Unequally sized errors, Non-convex optimization, Re-weighted least-squares
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 263293
URI: http://eprints.soton.ac.uk/id/eprint/263293
ISSN: 0167-9473
PURE UUID: ea65d65f-0f45-427f-b238-530b2ebeb91c

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Date deposited: 06 Jan 2007
Last modified: 14 Mar 2024 07:28

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Contributors

Author: I. Markovsky
Author: M. Rastello
Author: P. Premoli
Author: S. Van Huffel
Editor: J. Barlow

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