无需信源数先验的快速稀疏增强DOA估计方法  

Fast Sparse Enhanced DOA Estimation Method Without Source Number Priors

作　　者：高一丁 吴敏 郝程鹏[1,2] 吴永清 王立辉[3] GAO Yiding;WU Min;HAO Chengpeng;WU Yongqing;WANG Lihui(Institute of Acoustics,Chinese Academy of Sciences,Beijing 100190,China;College of Electronics,Electrical and Telecommunications Engineering,University of Chinese Academy of Sciences,Beijing 100049,China;Key Laboratory of Micro-inertial Instrument and Advanced Navigation Technology,Ministry of Education,School of Instrument Science and Engineering,Southeast University,Nanjing Jiangsu 210096,China)

机构地区：[1]中国科学院声学研究所,北京100190 [2]中国科学院大学电子电气与通信工程学院,北京100049 [3]东南大学仪器科学与工程学院微惯性仪表与先进导航技术教育部重点实验室,江苏南京210096

出　　处：《海军航空大学学报》2024年第5期515-522,共8页Journal of Naval Aviation University

基　　金：国家自然科学基金(62371446、61971412、62101603、62201623、62071460);中国科学院青年创新促进会(2023030)。

摘　　要：文章提出了一种无需信源数先验的超分辨波达方向(Direction of Arrival,DOA)估计方法,该方法利用稀疏增强的原子范数形式重新表征信号稀疏度,利用对数-行列式函数建立原子范数与l0原子范数的平滑关系,并通过泰勒展开形式简化其优化过程,以求解一个新的迭代加权优化问题为目标,使优化结果更加稀疏和精确;基于增强稀疏结果的信号重构Capon空间谱,从而在不需要信源先验的情况下,也可以准确估计目标的DOA。文章还针对这一特殊的迭代加权优化问题,给出了一种基于原对偶内点法的快速优化流程,问题中特殊的Toeplitz矩阵结构可以通过快速傅里叶变换技术提高计算效率。理论推导证明了该算法相较于CVX等凸优化工具,具有更快的计算效率,并且能够在信号数目未知的情况下,利用较少的快拍数实现高精度的DOA估计,具有很好的鲁棒性。实验仿真验证了该算法的有效性。A super-resolution direction of arrival(DOA)estimation method that does not require prior knowledge of the number of signal sources is proposed.The proposed method utilizes a reweighted atomic norm to recharacterize signal sparsity and employs a logarithmic-determinant function to establish a smooth relationship between the atomic norm and the atomic norm.By using a Taylor series expansion,the optimization process is simplified,aiming to solve a new iterative reweighted optimization problem,thereby achieving more sparse and accurate results.Based on the enhanced sparse results,the Capon spatial spectrum is reconstructed,allowing accurate DOA estimation without prior knowledge of the number of signal sources.Additionally,a fast optimization procedure based on the primal-dual interior-point method is provided for this special iterative reweighted optimization problem.The unique Toeplitz matrix structure in the problem is efficiently solved using Fast Fourier Transform techniques,improving computational efficiency.Theoretical analysis demonstrates that this algorithm offers faster computational efficiency compared to convex optimization tools like CVX and achieves high-precision DOA estimation with fewer snapshots,even when the number of signals is unknown,exhibiting robust performance.Experimental simulations validate the effectiveness of the proposed algorithm.

关 键 词：波达方向估计 连续压缩感知 Toeplitz结构矩阵 快速优化求解 

分 类 号：TP911.7[自动化与计算机技术]