We study the problem of signal source localization using angle of arrival (AOA) measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model's asymptotic localizability. Then we establish the consistency and asymptotic efficiency of the maximum likelihood (ML) estimator. However, obtaining the ML estimator is challenging due to its association with a non-convex optimization problem. To address this, we propose an asymptotically efficient two-step estimator that matches the ML estimator's asymptotic properties while achieving low computational complexity (linear in the number of measurements). The primary challenge lies in obtaining a consistent estimator in the first step. To achieve this, we construct a linear least squares problem through algebraic operations on the measurement nonlinear model to first obtain a biased closed-form solution. We then eliminate the bias using the data to yield an asymptotically unbiased and consistent estimator. In the second step, we perform a single Gauss-Newton iteration using the preliminary consistent estimator as the initial value, achieving the same asymptotic properties as the ML estimator. Finally, simulation results demonstrate the superior performance of the proposed two-step estimator for large sample sizes.

翻译：我们研究了利用到达角测量进行信号源定位的问题。首先，我们提出了传感器部署的可验证几何条件，以确保模型的渐近可定位性。随后，我们建立了最大似然估计器的一致性与渐近有效性。然而，由于最大似然估计器与非凸优化问题相关，其求解具有挑战性。为解决此问题，我们提出了一种渐近有效的两步估计器，该估计器在保持最大似然估计器渐近性质的同时，实现了较低的计算复杂度（与测量数量呈线性关系）。主要挑战在于第一步获得一致估计器。为此，我们通过对测量非线性模型进行代数运算构造线性最小二乘问题，首先获得有偏闭式解。随后，我们利用数据消除偏差，得到渐近无偏且一致的估计器。第二步中，我们以初步一致估计器作为初始值执行单次高斯-牛顿迭代，实现了与最大似然估计器相同的渐近性质。最后，仿真结果表明所提出的两步估计器在大样本量下具有优越性能。