State estimation using interval analysis and belief function theory: Application to dynamic vehicle localization
Résumé
A new approach to non-linear state estimation based on belief function theory and interval analysis is presented. This method uses belief structures composed of a finite number of axis-aligned boxes with associated masses. Such belief structures can represent partial information on model and measurement uncertainties, more accurately than can the bounded error approach alone. Focal sets are propagated in system equations using interval arithmetics and constraint satisfaction techniques, thus generalizing pure interval analysis. This model was used to locate a land vehicle using a dynamic fusion of GPS measurements with dead reckoning sensors. The method has been shown to provide more accurate estimates of vehicle position than does the bounded error method while retaining what is essential: providing guaranteed computations. The performances of our method were also slightly better than those of a particle filter, with comparable running time. These results suggest that our method is a viable alternative to both bounded error and probabilistic Monte-Carlo approaches for vehicle localization applications.
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