A Theoretical Framework for Relative Localization

Exploring the relative positions is a key issue in many emerging location-aware applications such as autonomous driving and formation control, where there exists no infrastructure to provide the absolute position information. In this paper, we establish a theoretical framework to address the state estimation problems in relative localization networks. In particular, we introduce the relative error for state estimates based on the concept of the equivalent state class, and apply the Fisher information analysis to derive the performance bounds. Then we present how measurement uncertainties influence the performance limits in the relative localization networks with self-measurements, after which our framework is extended to the scenarios with clock asynchronization and temporal cooperation. Finally, the connection between the theoretical foundation and the algorithm design is illustrated to provide insights into the operations in practical relative localization networks.