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）被广泛用于无人机（UAV）定位中定位无线信号发射源。与接收信号强度（RSS）和到达时间（TOA）相比，AOA具有更高的精度，且对分布式传感器的时间同步不敏感。然而，针对三维（3-D）场景的研究较少。此外，尽管最大似然估计（MLE）性能相对较高，但其计算复杂度极高，难以在实际应用中部署。本文提出了两种基于多平面几何中心的无人机三维AOA定位方法。第一种方法通过寻找内切球中心（CIS）可同时估计信源位置和角度测量噪声。首先，每个传感器测量两个角度（方位角和仰角），并据此构建两个平面。然后，通过寻找对应内切球中心与半径，获得信源位置和角度噪声的估计值。第二种算法称为MSD-LS，它去除了半径估计，虽无法估计角度噪声但计算复杂度更低。理论分析和仿真结果表明，所提方法能够趋近克拉美-罗下界（CRLB），且复杂度低于MLE。