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In this paper we derive a new capability for robots to measure relative direction, or Angle-of-Arrival (AOA), to other robots, while operating in non-line-of-sight and unmapped environments, 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 in the team, which we term as an AOA profile. The key intuition behind our approach is to emulate antenna arrays in the air as a robot moves freely in 2D or 3D space. The small differences in the phase and amplitude of WiFi signals are thus processed with knowledge of a robots’ local displacements (often provided via inertial sensors) to obtain the profile, via a method akin to Synthetic Aperture Radar (SAR). The main contribution of this work is the development of i) a framework to accommodate arbitrary 2D and 3D trajectories, as well as continuous mobility of both transmitting and receiving robots, while computing AOA profiles between them and ii) an accompanying analysis that provides a lower bound on variance of AOA estimation as a function of robot trajectory geometry that is based on the Cramer Rao Bound and antenna array theory. This is a critical distinction with previous work on SAR that restricts robot mobility to prescribed motion patterns, does not generalize to the full 3D space, and/or requires transmitting robots to be static during data acquisition periods. In fact, we find that allowing robots to use their full mobility in 3D space while performing SAR, results in more accurate AOA profiles and thus better AOA estimation. We formally characterize 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 on air/ground robot platforms. Our experimental results bolster our theoretical findings, demonstrating that 3D trajectories provide enhanced and consistent accuracy, with AOA error of less than 10 deg for 95% of trials. We also show that our formulation can be used with an off-the-shelf trajectory estimation sensor (Intel RealSense T265 tracking camera), for estimating the robots’ local displacements, and we provide theoretical as well as empirical results that show the impact of typical trajectory estimation errors on the measured AOA. Finally, we demonstrate the performance of our system on a multi-robot task where a heterogeneous air/ground pair of robots continuously measure AOA profiles over a WiFi link to achieve dynamic rendezvous in an unmapped, 300 square meter environment with occlusions.