Probabilistic techniques (such as Extended Kalman Filter and Particle Filter) have long been used to solve robotic localization and mapping problem. Despite their good performance in practical applications, they could suffer inconsistency problems. This paper proposes an interval analysis based method to estimate the vehicle pose (position and orientation) in a consistent way, by fusing low cost sensors and map data. We cast the localization problem into an Interval Constraint Satisfaction Problem (ICSP), solved via Interval Constraint Propagation (ICP) techniques. An interval map is built when a vehicle embedding expensive sensors navigates around the environment. Then vehicles with low cost sensors (dead reckoning and monocular camera) can use this map for ego-localization. Experimental results show the soundness of the proposed method in achieving consistent localization.