Least squares parameter estimation and multi-innovation least squares methods for linear fitting problems from noisy data

Least squares is an important method for solving linear fitting problems and quadratic optimization problems. This paper explores the properties of the least squares methods and the multi-innovation least squares methods. It demonstrates lemmas and theorems about the least squares and multi-innovati...

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Published inJournal of computational and applied mathematics Vol. 426; p. 115107
Main Author Ding, Feng
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2023
Subjects
Least squares
Least squares review
Least squares survey
Multi-innovation identification
Parameter estimation
System identification
Least squares review
Parameter estimation
System identification
Multi-innovation identification
Least squares survey
Least squares
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Abstract Least squares is an important method for solving linear fitting problems and quadratic optimization problems. This paper explores the properties of the least squares methods and the multi-innovation least squares methods. It demonstrates lemmas and theorems about the least squares and multi-innovation least squares parameter estimation algorithms after reviewing and surveying some important contributions in the area of system identification, such as the auxiliary model identification idea, the multi-innovation identification theory, the hierarchical identification principle, the coupling identification concept and the filtering identification idea. The results of the least squares and multi-innovation least squares algorithms for linear regressive systems with white noises can be extended to other systems with colored noises.
AbstractList Least squares is an important method for solving linear fitting problems and quadratic optimization problems. This paper explores the properties of the least squares methods and the multi-innovation least squares methods. It demonstrates lemmas and theorems about the least squares and multi-innovation least squares parameter estimation algorithms after reviewing and surveying some important contributions in the area of system identification, such as the auxiliary model identification idea, the multi-innovation identification theory, the hierarchical identification principle, the coupling identification concept and the filtering identification idea. The results of the least squares and multi-innovation least squares algorithms for linear regressive systems with white noises can be extended to other systems with colored noises.
ArticleNumber 115107
Author Ding, Feng
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  organization: School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan 430068, PR China
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Keywords Least squares review
Parameter estimation
System identification
Multi-innovation identification
Least squares survey
Least squares
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Snippet Least squares is an important method for solving linear fitting problems and quadratic optimization problems. This paper explores the properties of the least...
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StartPage 115107
SubjectTerms Least squares
Least squares review
Least squares survey
Multi-innovation identification
Parameter estimation
System identification
Title Least squares parameter estimation and multi-innovation least squares methods for linear fitting problems from noisy data
URI https://dx.doi.org/10.1016/j.cam.2023.115107
Volume 426
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