Gauss-Newton methods for robust parameter estimation

• Verfasst von: Binder, Tanja [VerfasserIn]
• Verfasst von: Kostina, Ekaterina [VerfasserIn]
• Titel: Gauss-Newton methods for robust parameter estimation
• Verf.angabe: Tanja Binder and Ekaterina Kostina
• Jahr des Originals: 2012
• Umfang: 33 S.
• Fussnoten: First online: 03 August 2012 ; Gesehen am 15.06.2018
• Titel Quelle: Enthalten in: Model Based Parameter Estimation
• Jahr Quelle: 2013
• Band/Heft Quelle: (2013), S. 55-87
• ISBN Quelle: 978-3-642-30367-8
• ISBN Quelle: 1-299-33664-7
• ISBN Quelle: 978-1-299-33664-3
• DOI: doi:10.1007/978-3-642-30367-8_3
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1576402282

Abstract

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.