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Recursive Robust Minimax Estimation

In: Bounding Approaches to System Identification

Author

Listed:
  • É. Walter

    (CNRS École Supérieure d’Électricité, Laboratoire des Signaux et Systèmes)

  • H. Piet-Lahanier

    (SM Office National d’Études et de Recherches Aérospatiales, Direction des Études de Synthèse)

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.

Suggested Citation

  • É. Walter & H. Piet-Lahanier, 1996. "Recursive Robust Minimax Estimation," Springer Books, in: Mario Milanese & John Norton & Hélène Piet-Lahanier & Éric Walter (ed.), Bounding Approaches to System Identification, chapter 12, pages 183-197, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-9545-5_12
    DOI: 10.1007/978-1-4757-9545-5_12
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