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The structured total least-squares approach for non-linearly structured matrices

✍ Scribed by P. Lemmerling; S. Van Huffel; B. De Moor

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
109 KB
Volume
9
Category
Article
ISSN
1070-5325

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✦ Synopsis

Abstract

In this paper, an extension of the structured total least‐squares (STLS) approach for non‐linearly structured matrices is presented in the so‐called ‘Riemannian singular value decomposition’ (RiSVD) framework. It is shown that this type of STLS problem can be solved by solving a set of Riemannian SVD equations. For small perturbations the problem can be reformulated into finding the smallest singular value and the corresponding right singular vector of this Riemannian SVD. A heuristic algorithm is proposed. Some examples of Vandermonde‐type matrices are used to demonstrate the improved accuracy of the obtained parameter estimator when compared to other methods such as least squares (LS) or total least squares (TLS). Copyright © 2002 John Wiley & Sons, Ltd.

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