The element-wise weighted total least squares problem

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.


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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.

Item Type: Article
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Keywords: Total least squares; Multivariate errors-in-variables model; Unequally sized errors; Non-convex optimization; Re-weighted least-squares
Divisions: Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Comms, Signal Processing & Control
ePrint ID: 263293
Date Deposited: 06 Jan 2007
Last Modified: 27 Mar 2014 20:07
Publisher: Elsevier
Further Information:Google Scholar
ISI Citation Count:19

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