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Optimization and Engineering
Published in: Optimization and Engineering 3/2014

01-09-2014

A general approach of least squares estimation and optimal filtering

Author: Benjamin Lenoir

Published in: Optimization and Engineering | Issue 3/2014

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Abstract

The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the method as well as numerical considerations are discussed. Then two particular cases are considered: the usual least squares method and the Generalized Least Squares method. In both cases, the estimator and its variance are characterized in the time domain and in the Fourier domain. Finally, the equivalence of the Generalized Least Squares method and the optimal filtering technique using a matched filter is established.
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Footnotes
1
As stated by the Wiener-Khintchine theorem, S is the Fourier transform of R (Lampard 1954).
 
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Metadata
Title
A general approach of least squares estimation and optimal filtering
Author
Benjamin Lenoir
Publication date
01-09-2014
Publisher
Springer US
Published in
Optimization and Engineering / Issue 3/2014
Print ISSN: 1389-4420
Electronic ISSN: 1573-2924
DOI
https://doi.org/10.1007/s11081-013-9217-7

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