In this paper we derive a new capability for robots to measure relative direction, or Angle-of-Arrival (AOA), to other robots operating in non-line-of-sight and unmapped environments with occlusions, without requiring external infrastructure. We do so by capturing all of the paths that a WiFi signal traverses as it travels from a transmitting to a receiving robot, which we term an AOA profile. The key intuition is to emulate antenna arrays in the air as the robots move in 3D space, a method akin to Synthetic Aperture Radar (SAR). The main contributions include development of i) a framework to accommodate arbitrary 3D trajectories, as well as continuous mobility all robots, while computing AOA profiles and ii) an accompanying analysis that provides a lower bound on variance of AOA estimation as a function of robot trajectory geometry based on the Cramer Rao Bound. This is a critical distinction with previous work on SAR that restricts robot mobility to prescribed motion patterns, does not generalize to 3D space, and/or requires transmitting robots to be static during data acquisition periods. Our method results in more accurate AOA profiles and thus better AOA estimation, and formally characterizes this observation as the informativeness of the trajectory; a computable quantity for which we derive a closed form. All theoretical developments are substantiated by extensive simulation and hardware experiments. We also show that our formulation can be used with an off-the-shelf trajectory estimation sensor. Finally, we demonstrate the performance of our system on a multi-robot dynamic rendezvous task.
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