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Gauss-Newton methods for robust parameter estimation

In this paper we treat robust parameter estimation procedures for problems constrained by differential equations. Our focus is on the l 1 norm estimator and Huber’s M-estimator. Both of the estimators are briefly characterized and the corresponding optimality conditions are given. We describe the so...

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Bibliographische Detailangaben
Hauptverfasser: Binder, Tanja (VerfasserIn) , Kostina, Ekaterina (VerfasserIn)
Dokumenttyp: Kapitel/Artikel Konferenzschrift
Sprache:Englisch
Veröffentlicht: 2013
In: Model Based Parameter Estimation
Year: 2012, Pages: 55-87
DOI:10.1007/978-3-642-30367-8_3
Schlagworte:
Konferenzschrift
Online-Zugang:Verlag, Volltext: http://dx.doi.org/10.1007/978-3-642-30367-8_3
Verlag, Volltext: https://link.springer.com/chapter/10.1007/978-3-642-30367-8_3
Volltext
Verfasserangaben:Tanja Binder and Ekaterina Kostina

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520 |a In this paper we treat robust parameter estimation procedures for problems constrained by differential equations. Our focus is on the l 1 norm estimator and Huber’s M-estimator. Both of the estimators are briefly characterized and the corresponding optimality conditions are given. We describe the solution of the resulting minimization problems using the Gauss-Newton method and present local convergence results for both nonlinear constrained l 1 norm and Huber optimization. An approach for the efficient solution of the linearized problems of the Gauss-Newton iterations is also sketched as well as globalization strategies using line search methods. Two numerical examples are exercised to demonstrate the superiority of the two presented robust estimators over standard least squares estimation in case of outliers in the measurement data. 
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