修正极坐标系中基于AOA的近似无偏定位方法

An Approximately Unbiased Method for AOA-Based Localization in Modified Polar Representation

提出了一种基于到达角(Angle-of-Arrival,AOA)测量值的近远场统一定位方法。使用修正极坐标(Modified Polar Representation,MPR)代替了传统的笛卡尔坐标来表示目标源坐标,以避免目标源位于远场时的数值问题。将基于AOA的定位问题描述为约束加权最小二乘(Constrained Weighted Least Squares,CWLS)问题,并通过拉格朗日乘子法和特征值分解获得该问题的闭式解。该方法无需已知目标源位于近场或远场的先验知识,就可获得近场时目标源的坐标以及远场时目标源方位角和俯仰角的准确估计。但在这一过程中由于模型近似导致了较大的估计偏差。为了解决这一问题,进一步推导了CWLS估计的理论偏差,并将其从闭式解中减去,以获得近似无偏的估计。仿真实验表明该近似无偏估计方法能够达到克拉美-罗下界(Cramer-Rao Lower Bound,CRLB)。

We propose a unified near-field and far-field localization method using angle of arrival(AOA)measurements. Instead of using the traditional Cartesian coordinates,we use the modified polar representation(MPR)of the source position to avoid the numerical problem when the source lies in the far field. By so doing,the AOA-based localization problem is formulated into a constrained weighted least squares(CWLS)problem. The closed-form solution of the CWLS problem is obtained through Lagrange multiplier method and eigenvalue decomposition. The proposed method is able to provide accurate estimates of the source position coordinates in the near field and source azimuth and elevation angles in the far field,without knowing the a priori knowledge that the source lies in near or far field. However,the model approximation causes bias in the estimation. To deal with this problem,we further derive the theoretical bias of the CWLS problem,which is then subtracted from the CWLS solution to obtain an approximately unbiased estimate. Simulation experiments show that the proposed method is able to reach the Cramer-Rao lower bound(CRLB)accuracy when the noise is not too large.