Angle of arrival (AOA) is widely used to locate a wireless signal emitter in unmanned aerial vehicle (UAV) localization. Compared with received signal strength (RSS) and time of arrival (TOA), it has higher accuracy and is not sensitive to time synchronization of the distributed sensors. However, there are few works focused on three-dimensional (3-D) scenario. Furthermore, although maximum likelihood estimator (MLE) has a relatively high performance, its computational complexity is ultra high. It is hard to employ it in practical applications. This paper proposed two multiplane geometric center based methods for 3-D AOA in UAV positioning. The first method could estimate the source position and angle measurement noise at the same time by seeking a center of the inscribed sphere, called CIS. Firstly, every sensor could measure two angles, azimuth angle and elevation angle. Based on that, two planes are constructed. Then, the estimated values of source position and angle noise are achieved by seeking the center and radius of the corresponding inscribed sphere. Deleting the estimation of the radius, the second algorithm, called MSD-LS, is born. It is not able to estimate angle noise but has lower computational complexity. Theoretical analysis and simulation results show that proposed methods could approach the Cramer-Rao lower bound (CRLB) and have lower complexity than MLE.

翻译：到达角（AOA）广泛应用于无人机（UAV）定位中的无线信号发射源定位。与接收信号强度（RSS）和到达时间（TOA）相比，AOA具有更高精度，且对分布式传感器的时间同步不敏感。然而，目前针对三维（3-D）场景的研究较少。此外，尽管最大似然估计器（MLE）具有较高性能，但其计算复杂度极高，难以在实际应用中使用。本文提出了两种基于多平面几何中心的方法用于无人机定位中的三维AOA。第一种方法通过寻找内切球中心（CIS）同时估计信号源位置和角度测量噪声。首先，每个传感器可测量两个角度：方位角和仰角，并据此构建两个平面。随后，通过寻找对应内切球的中心和半径，获得信号源位置和角度噪声的估计值。删除半径估计后得到第二种算法MSD-LS，该算法虽无法估计角度噪声，但计算复杂度更低。理论分析与仿真结果表明，所提方法能够逼近克拉美-罗下界（CRLB），且复杂度低于MLE。