Fundamental Limits for Joint Relative Position and Orientation Estimation

Multi-agent robotic systems, also called robotic swarms, are a promising technology for extra- terrestrial exploration. Autonomous operation of such swarms requires reliable navigation, where not only the position but also the agents' orientation relative to each other is of interest. Extracting both angle and range information from radio signals, e.g. by using antenna arrays, avoids the rigidity constraint and allows positioning for arbitrary geometries. A joint position and orientation solution can still be obtained for agents connected by a single link. The aim of this paper is to derive the fundamental limit for joint position and orientation estimation for the anchor-free case. To obtain a fundamental limit, we derive the Cramér-Rao bound (CRB) directly based on the received signal. Our results show that, even when the agents' orientations are unknown, angle information is beneficial for position estimation at short to medium distances.