Estimation ensembliste par analyse par intervalles Application à la localisation d'un véhicule

Abstract : In this work, we develop tools based on interval analysis with application to estimation and control. We are interested more particularly in the parameter and state estimation for non-linear models. For the identification, Hansen's global optimisation algorithm provides a enclosure of all the values of the vectors of parameters minimizing a cost function involving measurements on a real device that has to be modelled and the measurements predicted by the model. We show that this can evidence possible identifiability problems without preliminary study. In the bounded-error approach, even in presence of outliers, inner and outer approximations of the sets of acceptable parameter vectors are provided by the set inversion algorithms using interval analysis. When the bounds on the errors are not known, an original method evaluating the smallest error bounds providing a nonempty set of acceptable vector of parameters is proposed. A new recursive algorithm for guaranteed state estimation is presented. It has a structure similar to the Kalman filter, but in a bounded-error context, at any time instant, it provides a set containing the values of the state compatible with information available. This algorithm is built using a set inversion algorithm and an original algorithm for the evaluation of the direct image of a set by a function. Both exploit the concept of subpavings described by binary trees, which allows an approximate description of compact sets. These techniques are applied to the localization and tracking of a robot inside a charted room. The presence of outliers, as well as ambiguities related to symmetries of the part of the room in which the robot is, are taken into account without difficulty. Possible non-connected sets of configurations can be considered and their treatment does not pose any problem. Moreover, the tracking, even in the presence of outliers, is made in real time on the treated examples.
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Automatic. Université Paris Sud - Paris XI, 1999. French


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Submitted on : Friday, April 16, 2010 - 3:23:42 PM
Last modification on : Friday, April 16, 2010 - 4:56:49 PM

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Michel Kieffer. Estimation ensembliste par analyse par intervalles Application à la localisation d'un véhicule. Automatic. Université Paris Sud - Paris XI, 1999. French. <tel-00473805>

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