Mobility applications highly depend on accurate and reliable localization, as well as mapping of the surroundings where one is moving. For safety critical applications like highly automated vehicles, localization and mapping enable many actors not only making their own local dynamic map, but also sharing the information in order to update this map cooperatively with the others. This book investigates a deterministic filtering technique, based on interval analysis and constraint propagation, to deal with the robotic localization and mapping issues, with certain advantages among which reliability. Both practical and theoretical aspects of the vehicle localization and mapping problems are modeled and exploited. Some new deterministic methods using interval analysis and constraint propagation are presented, accompanied with sufficient simulation and full-scale experimental data to illustrate the applicability of the method and its reliability. This book contains also an effectively pedagogical presentation for understanding and using interval analysis and constraint propagation to solve practical problems, which is very helpful for a beginer in the domain.