On the impact of a priori information on localization accuracy and complexity

Accuracy and complexity represent fundamental aspects of localization and tracking systems. In this manuscript the impact of a priori knowledge about agent position on the accuracy and the complexity of localization algorithms is investigated. In particular, first Cramer-Rao bounds on localization accuracy are derived under the assumption that a priori information is described by a map restricting the agent position to a specific region. Then, the computational complexity of optimal map-aware and map-unaware localization techniques is assessed. Our results evidence that: a) map-aware localization accuracy can be related to some geometrical features of the map but usually exhibits a complicated dependence on them; b) in some scenarios map-aware localization algorithms provide better accuracy than their map-unaware counterparts at comparable computational complexity.