Impact of 3D Antenna Radiation Patterns on TDOA-Based Wireless Localization of UAVs

Next big commercial applications of drones require to fly the drone beyond the visual line of sight (BVLOS). This inevitable ability to fly BVLOS will also necessitate the ability to keep track of the drone's location, in order to ensure successful completion of the intended service. In this context, we explore the fundamental limits of 3D localization of drones in conjunction with the effects of the 3D antenna radiation patterns. Although the localization of drone/unmanned aerial vehicle (UAV) is a well-studied topic in the literature, its relationship to the antenna effects remains mostly unexplored. In this paper, we investigate the impact of antenna radiation pattern on the accuracy of time-difference-of-arrival (TDOA)-based localization of the UAV. Specifically, we consider a scenario where a fixed number of radio-frequency (RF) sensors, placed at some known locations on the ground, collect the TDOA measurements from the signals transmitted from the UAV and estimate the location of the UAV from these observations. In order to study the impact of the antenna effects on the fundamental limits of the TDOA-based positioning scheme, we develop a simple analytical model to approximate the total antenna gains experienced by an air-to-ground (A2G) link, for various orientations of the antennas. We then derive the Cramer-Rao lower bound for the TDOA based localization scheme, for all three combinations of the transmit and the receive antenna orientations: vertical-vertical (VV), horizontal-horizontal (HH), and vertical-horizontal (VH).