Interval analysis for non-linear parameter and state estimation: contributions and limitations

Michel Kieffer 1, 2, 3 Eric Walter 1 Isabelle Braems 4 Luc Jaulin 5, 6, 7
1 L2S - Laboratoire des signaux et systèmes
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 IUF - Institut Universitaire de France
4 LEMHE - Laboratoire d'étude des matériaux hors équilibre
5 STIC - Pôle STIC [Brest]
6 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
7 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés
Abstract : Parameter or state estimation should take into account the fact that the model is an approximation of reality and that the data are corrupted by noise. In this paper, each uncertain quantity is assumed to belong to a known set. The problem, known as parameter or state bounding, is the to characterize the set of all parameter or state vectors that are consistent with the model structure, data and error bounds. A description of how interval analysis can be used to find guaranteed estimates in a nonlinear context is provided. The main notions of interval analysis are first recalled very briefly. the simpler problem of parameter estimation is then considered. State estimation, which contains parameter tracking as a special case, is treated next. A simple illustrative example is finally presented.
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Michel Kieffer, Eric Walter, Isabelle Braems, Luc Jaulin. Interval analysis for non-linear parameter and state estimation: contributions and limitations. NOLCOS 2001: 5th IFAC Symposium Nonlinear and Control Systems, Jul 2001, Saint-Petersburg, Russia. ⟨hal-00845405⟩

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