Probabilistic approaches are extensively used to solve high-dimensionality problems in many different fields. The particle filter is a prominent approach in the field of Robotics, due to its adaptability to non-linear models with multi-modal distributions. Nonetheless, its result is strongly dependent on the quality and the number of samples required to cover the space of possible solutions. In contrast, interval analysis deals with high-dimensionality problems by reducing the space enclosing the actual solution. Notwithstanding, it cannot precise where in the resulting subspace the actual solution is. We devised a strategy that combines the best of both worlds. Our approach is illustrated by solving the global localization problem for underwater robots.