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Recursive Robust Minimax Estimation

  • Chapter
Bounding Approaches to System Identification

Abstract

An important problem arising when one wants to estimate the parameters of a model in a bounded-error context is the specification of reliable bounds for this error. In early phases of development, when no prior information is available, one may wish to know the minimum upper bound for the amplitude of the error such that the feasible parameter set is not empty. This corresponds to using a minimax estimator. For models linear in their parameters, we describe a method that takes advantage of a reparametrization in order to recursively obtain the minimax estimates and associated bounds for the error. It also provides the set of parameters compatible with any upper bound of the error. This procedure is extended to output-error models, which are nonlinear in their parameters. Its robustness to outliers is discussed and a technique is described to detect and discard them.

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Author information

Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS École Supérieure d’Électricité, 91192, Gif-sur-Yvette Cedex, France

    É. Walter

  2. Direction des Études de Synthèse, SM Office National d’Études et de Recherches Aérospatiales, F-92322, Châtillon Cedex, France

    H. Piet-Lahanier

Authors
  1. É. Walter
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  2. H. Piet-Lahanier
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Editor information

Editors and Affiliations

  1. Dipartimento di Automatica e Informatica, Politecnico di Torino, Torino, 10129, Italy

    Mario Milanese

  2. School of Electronic and Electrical Engineering, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

    John Norton

  3. Direction des Études de Synthèse, SM Office National d’Études et de Recherches Aérospatiales, Châtillon Cedex, F-92322, France

    Hélène Piet-Lahanier

  4. Laboratoire des Signaux et Systèmes, CNRS-École Supérieure d’Électricité, Gif-sur-Yvette Cedex, 91192, France

    Éric Walter

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© 1996 Springer Science+Business Media New York

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Walter, É., Piet-Lahanier, H. (1996). Recursive Robust Minimax Estimation. In: Milanese, M., Norton, J., Piet-Lahanier, H., Walter, É. (eds) Bounding Approaches to System Identification. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9545-5_12

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  • DOI: https://doi.org/10.1007/978-1-4757-9545-5_12

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9547-9

  • Online ISBN: 978-1-4757-9545-5

  • eBook Packages: Springer Book Archive

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