基于迭代原子范数最小化的均匀圆阵方位估计

doi:10.12305/j.issn.1001-506X.2025.06.03

摘要/Abstract

摘要：

针对水下阵列波达方位(direction of arrival, DOA)估计在少快拍情况下对相邻声源分辨能力差的问题，提出了基于迭代原子范数最小化的均匀圆环阵DOA快速估计方法。所提方法利用模态域处理方法对阵列流形进行预处理，将均匀圆环阵转换为虚拟直线阵，然后通过对角重构估计无噪接收信号协方差矩阵，消除模态域处理引入的非均匀噪声的影响。为了充分利用接收信号稀疏性，同时避免字典网格搜索带来的误差，在模态域引入迭代原子范数最小化稀疏恢复方法，提出均匀圆环阵迭代原子范数最小化(uniform circular array-iterative atomic norm minimization, UCA-IANM)方位估计方法。原子范数最小化稀疏恢复问题一般采用内点法求解，该方法随接收信号快拍数增加，计算量急剧上升，不适用于水下计算资源受限的场景。在交替方向乘子法(alternating direction multiplier method, ADMM)的基础上，针对正则化参数难以选择的问题，提出了基于参数优化ADMM的UCA-IANM(UCA-IANM assisted by ADMM with parameter optimization, UCA-IANM-APO)DOA快速估计算法。仿真实验与实测数据分析表明，UCA-IANM-APO DOA快速估计方法的角度分辨能力和估计精度均优于传统DOA估计方法，求解速度较内点法提升了两个数量级。

关键词: 均匀圆环阵, 虚拟成阵, 对角重构, 原子范数最小化, 交替方向乘子法

Abstract:

To address the challenge of underwater array direction of arrival (DOA) estimation of poor discrimination between adjacent sound sources when only a few snapshots are available, a fast estimation method based on iterative atomic norm minimization (IANM) is proposed for estimating the DOA for uniform circular arrays. To reduce the impact of non-uniform noise caused by modal domain processing, the proposed method preprocesses the array manifolds using the modal domain processing technique. This technique transforms the uniform circular array (UCA) into a virtual linear array and then estimates the covariance matrix of the received signal in the absence of noise through diagonal reconstruction. In order to make full use of the sparsity of the received signal and avoid the error caused by dictionary grid search, an IANM sparse recovery method is introduced in the modal domain, and the UCA-IANM direction estimation method is proposed. The sparse recovery problem of atomic norm minimization (ANM) is typically addressed using the interior point method, which leads to a sharp increase in workload as the number of received signal snapshots grows, making it unsuitable for scenarios with limited underwater computational resources. In this paper, based on the alternating direction multiplier method (ADMM), the UCA-IANM assisted by ADMM with parameter optimization (UCA-IANM-APO) DOA fast estimation method is proposed to address the challenge in selecting the regularization parameter. Simulation experiments and measured data demonstrate that the UCA-IANM-APO method has better angular resolution and estimation accuracy compared to the traditional DOA estimation methods, and the solution speed is improved by two orders of magnitude compared to the interior point method.

Key words: uniform circular array (UCA), virtual array, diagonal reconstruction, atomic norm minimization (ANM), alternating direction multiplier method

中图分类号:

江首德, 鄢社锋, 毛琳琳, 江春瑾. 基于迭代原子范数最小化的均匀圆阵方位估计[J]. 系统工程与电子技术, 2025, 47(6): 1746-1756.

Shoude JIANG, Shefeng YAN, Linlin MAO, Chunjin JIANG. Uniform circular array direction-of-arrival estimation based on iterative atomic norm minimization[J]. Systems Engineering and Electronics, 2025, 47(6): 1746-1756.

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算法名称	算法复杂度
UCA-IANM-CVX	$ O\left\{\varOmega_w \varOmega_{\mathrm{ANM}}\left(M_t^3+M_t^2+1\right)\right\}$
UCA-ANM-CVX	$ O\left\{\varOmega_{\mathrm{ANM}}\left[\left(M_t+K\right)^3+\left(M_t+K\right)^2+1\right]\right.$
UCA-IANM-APO	$ O\left\{\varOmega_w \varOmega_{\mathrm{ADMM}} M_t^3\right\}$

算法名称	耗时/s
UCA-IANM-CVX	25.160 2
UCA-ANM-CVX	2.645 1
UCA-IANM-APO	0.017 2

算法名称	主瓣宽度/(°)	旁瓣级/dB
UCA-RB-MUSIC	9	-13
UCA-IANM-CVX	1	-31
UCA-ANM-CVX	5	-19
UCA-IANM-APO	1	-31

算法名称	主瓣宽度/(°)	旁瓣级/dB
UCA-RB-MUSIC	18	-13
UCA-IANM-CVX	4	-25
UCA-ANM-CVX	7	-21
UCA-IANM-APO	4	-25

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