Iterative Sparse Covariance Matrix Fitting Direction of Arrival Estimation Method Based on Vector Hydrophone Array

基于矢量水听器阵的迭代稀疏协方差矩阵拟合波达方向估计方法

¹ School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China
² School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China

Received: 18 March 2019

Abstract

Aiming at the direction of arrival (DOA) estimation of coherent signals in vector hydrophone array, an iterative sparse covariance matrix fitting algorithm is proposed. Based on the fitting criterion of weighted covariance matrix, the objective function of sparse signal power is constructed, and the recursive formula of sparse signal power iteration updating is deduced by using the properties of Frobenius norm. The present algorithm uses the idea of iterative reconstruction to calculate the power of signals on discrete grids, so that the estimated power is more accurate, and thus more accurate DOA estimation can be obtained. The theoretical analysis shows that the power of the signal at the grid point solved by the present algorithm is preprocessed by a filter, which allows signals in specified directions to pass through and attenuate signals in other directions, and has low sensitivity to the correlation of signals. The simulation results show that the average error estimated by the present method is 39.4% of the multi-signal classification high resolution method and 73.7% of the iterative adaptive sparse signal representation method when the signal-to-noise ratio is 15 dB and the non-coherent signal. Moreover, the average error estimated by the present method is 12.9% of the iterative adaptive sparse signal representation method in the case of coherent signal. Therefore, the present algorithm effectively improves the accuracy of target DOA estimation when applying to DOA estimation with highly correlated targets.

摘要

针对矢量水听器阵列相干信号方位估计问题，提出了迭代稀疏协方差矩阵拟合波达方向估计（direction of arrival，DOA）算法。基于加权协方差矩阵拟合准则，构建了关于稀疏信号功率的目标函数，利用Frobenius范数性质推导了稀疏信号功率迭代更新的递推式。所提算法利用迭代重构的思想计算离散网格点上信号功率，使得估计的功率更精确，从而获得更加精确的DOA估计。理论分析表明，所提算法求解网格点上信号的功率经过了滤波器的预处理，该滤波器允许指定方向的信号通过并且衰减其他方向的信号，对信号的相关性具有较低的敏感度。仿真实验结果表明，在信噪比为15 dB，非相干信号情况下，所提方法估计的平均误差为多重信号分类高分辨方法的39.4%，迭代自适应稀疏信号表示方法的73.7%；相干信号情况下，所提方法估计的平均误差为迭代自适应稀疏信号表示方法的12.9%。所提算法应用于具有高度相关性目标的DOA估计时，可有效提高目标DOA估计的精度。