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Convergence properties of the generalised least squares identitication method

✍ Scribed by Torsten Söderström

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
816 KB
Volume
10
Category
Article
ISSN
0005-1098

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✦ Synopsis

Generalized least squares identification may be interpreted as a loss .function minimization, but more than one local minimum may exist, depending on the signal to noise ratio, and undesired estimates can result.

Summary--Convergence properties of the generalized least squares method are analyzed. The method can be interpreted as optimization of a likelihood function. The number of local maximum points of the likelihood function is examined. It is shown that this number is influenced by the signal to noise ratio. This theoretical result is illustrated by numerical examples using plant measurements. It is also proved that the method gives consistent estimates under suitable conditions. *

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✍ Henry L. Langhaar 📂 Article 📅 1969 🏛 Elsevier Science 🌐 English ⚖ 625 KB

For approximation problems involving residuals that are linear functions of the parameters, it is shown that the collocation approximation approaches the least-squares approximation