Zuo Le, Pan Jin, Ma Boyuan
Department of Microwave Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.
School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore.
Sensors (Basel). 2018 Apr 4;18(4):1088. doi: 10.3390/s18041088.
This paper essentially focuses on parameter estimation of multiple wideband emitting sources with time-varying frequencies, such as two-dimensional (2-D) direction of arrival (DOA) and signal sorting, with a low-cost circular synthetic array (CSA) consisting of only two rotating sensors. Our basic idea is to decompose the received data, which is a superimposition of phase measurements from multiple sources into separated groups and separately estimate the DOA associated with each source. Motivated by joint parameter estimation, we propose to adopt the expectation maximization (EM) algorithm in this paper; our method involves two steps, namely, the expectation-step (E-step) and the maximization (M-step). In the E-step, the correspondence of each signal with its emitting source is found. Then, in the M-step, the maximum-likelihood (ML) estimates of the DOA parameters are obtained. These two steps are iteratively and alternatively executed to jointly determine the DOAs and sort multiple signals. Closed-form DOA estimation formulae are developed by ML estimation based on phase data, which also realize an optimal estimation. Directional ambiguity is also addressed by another ML estimation method based on received complex responses. The Cramer-Rao lower bound is derived for understanding the estimation accuracy and performance comparison. The verification of the proposed method is demonstrated with simulations.
本文主要聚焦于具有时变频率的多个宽带发射源的参数估计，例如二维到达方向（DOA）和信号分选，采用仅由两个旋转传感器组成的低成本圆形合成阵列（CSA）。我们的基本思路是将接收到的数据（即多个源的相位测量叠加）分解为不同的组，并分别估计与每个源相关的DOA。受联合参数估计的启发，我们在本文中提出采用期望最大化（EM）算法；我们的方法包括两个步骤，即期望步骤（E步）和最大化步骤（M步）。在E步中，找到每个信号与其发射源的对应关系。然后，在M步中，获得DOA参数的最大似然（ML）估计。这两个步骤迭代交替执行，以共同确定DOA并对多个信号进行分选。基于相位数据通过ML估计推导出闭式DOA估计公式，该公式也实现了最优估计。还通过基于接收复响应的另一种ML估计方法解决了方向模糊性问题。推导了克拉美罗下界以理解估计精度和性能比较。通过仿真验证了所提方法。
