Guaranteed robust nonlinear estimation with application to robot localization

Luc Jaulin (1, 2, 3) , Michel Kieffer (4, 5, 6) , Eric Walter (4) , Dominique Meizel (7)

1 STIC - Département STIC [Brest]
2 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
3 LISA - Laboratoire d'Ingéniérie des Systèmes Automatisés
4 L2S - Laboratoire des signaux et systèmes
5 LTCI - Laboratoire Traitement et Communication de l'Information
6 IUF - Institut universitaire de France
7 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

when rliable prior bounds on the acceptable erors between the data and corresponding model outputs are availabl, bounded-error estimation techniques make it possible to characterize the set of all acceptable parameter vectors in a guaranteed way, ven when the model is nonlinear and the number of data points small. However, when the data may contain outliers, i.e., data points for which these bounds should be violated, this set may turn out to be empty, or a least unrealistically small. The outlier minimal number estimator (OMNE) has been designed to deal with such a situation, by minimizing the number of data points considered as outliers. OMNE has been shown in previous papers to be remarkbly robust, even to a majority of outliers. Up to now, it was implemented by random scanning, so its results could not be guaranteed. In this paper, a new algorithm based on set inversion via interval analysis provides a guaranteed OMNE, which is applied to the initial localization of an actual robot in a partially known 2D environment. The difficult problems of associating range data to landmarks of the environment and of detecting potential outliers are solved as by-products of the procedure.

Mots clés: bounded-error etsimation; interval analysis; nonlinear estimation; outliers; robot localization; robust estimation; set estimation; set inversion

Domaines: Sciences de l'ingénieur [physics]

Luc Jaulin, Michel Kieffer, Eric Walter, Dominique Meizel. Guaranteed robust nonlinear estimation with application to robot localization. IEEE transactions on systems, man, and cybernetics, 2002, 32 (4), pp.374-382. ⟨10.1109/TSMCC.2002.806747⟩. ⟨hal-00845581⟩