Angle of arrival (AOA) is widely used to locate a wireless signal emitter. 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 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）广泛用于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具有更高精度，且对分布式传感器的时间同步不敏感。然而，针对三维场景的研究工作较少。此外，尽管最大似然估计器（MLE）性能相对较高，但其计算复杂度极高，难以应用于实际场景。本文提出两种基于多平面几何中心的三维AOA定位方法。第一种方法通过寻找内切球中心（CIS）同时估计源位置与角度测量噪声。首先，每个传感器可测量方位角和仰角两个角度，据此构建两个平面；然后通过寻找对应内切球的球心和半径获得源位置与角度噪声的估计值。去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算法。