A new approach to nonlinear 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 Global Positioning System 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.