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Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis

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  • Jaulin, Luc
  • Walter, Eric

Abstract

This paper deals with parameter estimation in the bounded-error context. A new approach, based on interval analysis, is proposed to compute guaranteed estimates of suitable characteristics of the set of all values of the parameter vector such that the error between the experimental data and the model outputs belongs to some predefined feasible set. This approach is especially suited to models whose output is nonlinear in their parameters, a situation where most available methods fail to provide any guarantee as to the global validity of the results obtained. After a brief presentation of interval analysis, an algorithm is proposed, which makes it possible to obtain guaranteed estimates of characteristics of such as its volume or the smallest axis-aligned box that contains it. Properties of this algorithm are established, and illustrated on a simple example.

Suggested Citation

  • Jaulin, Luc & Walter, Eric, 1993. "Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(2), pages 123-137.
    • Handle: RePEc:eee:matcom:v:35:y:1993:i:2:p:123-137
    DOI: 10.1016/0378-4754(93)90008-I
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    References listed on IDEAS

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    1. Moore, Ramon, 1992. "Parameter sets for bounded-error data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(2), pages 113-119.
    2. Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.
    3. Mo, S.H. & Norton, J.P., 1990. "Fast and robust algorithm to compute exact polytope parameter bounds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 481-493.
    4. Broman, V. & Shensa, M.J., 1990. "A compact algorithm for the intersection and approximation of N-dimensional polytopes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 469-480.
    5. Piet-Lahanier, H. & Walter, E., 1990. "Characterization of non-connected parameter uncertainty regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 553-560.
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    Cited by:

    1. Petrone, Giovanni & Spagnuolo, Giovanni & Zamboni, Walter & Siano, Raffaele, 2021. "An improved mathematical method for the identification of fuel cell impedance parameters based on the interval arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 183(C), pages 78-96.
    2. Jaulin, L. & Walter, E. & Lévêque, O. & Meizel, D., 2000. "Set inversion for χ-algorithms, with application to guaranteed robot localization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 52(3), pages 197-210.
    3. Norton, J.P., 1999. "Translation of bounds on time-domain behaviour of dynamical systems into parameter bounds for discrete-time rational transfer-function models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(4), pages 469-478.

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