基于M-FIPM的无网格DOA估计算法

doi:10.12305/j.issn.1001-506X.2022.02.09

摘要/Abstract

摘要：

针对目前快速内点法(fast interior point method, FIPM)无法处理多快拍情况下半正定规划(semi-definite programming, SDP)问题的缺陷, 提出一种基于多快拍FIPM(multiple snapshots FIPM, M-FIPM)的无网格波达方向(direction of arrival, DOA)估计算法。该算法首先对天线阵列接收多快拍数据的协方差矩阵进行特征值分解, 然后利用特征值和特征向量的相应加权和来重新构建符合FIPM模型的单快拍观测向量, 最后再通过FIPM获得SDP问题的最优解并以此建立Toeplitz矩阵, 根据该矩阵的Vandermonde分解结果便可以估计出入射信源的DOA参数。M-FIPM算法不仅保留了现有FIPM算法运算复杂度低的特点, 能够将SDP问题的维度由O(M²)降低为O(M), 同时在新单快拍观测向量的构造过程中, 由于舍弃了协方差矩阵小特征值所对应的部分, 因此能够有效抑制噪声对于后续DOA参数恢复过程的影响, 进一步提升算法的估计精度。仿真实验验证了M-FIPM在估计精度以及运算时间方面的优越性。

关键词: 原子范数最小化, 半正定规划, 无网格波达方向估计算法, 快速内点法

Abstract:

Given the defect that the fast interior point method (FIPM) cannot handle the semi-definite programming (SDP) problem in the case of multiple snapshots, a meshless direction of arrival (DOA) estimation algorithm based on multiple snapshots FIPM (multiple snapshots FIPM, M-FIPM) is proposed. The algorithm first decomposes the eigenvalue of the covariance matrix of the multi-snap data received by the antenna array, and then uses the corresponding weighted sum of the eigenvalues and eigenvectors to reconstruct the single-shot observation vector that conforms to the FIPM model, and finally obtains the SDP through FIPM. The optimal solution of the problem is used to establish the Toeplitz matrix. According to the Vandermonde decomposition result of the matrix, the DOA parameters of the incident source can be estimated. The M-FIPM algorithm not only retains the low computational complexity of the existing FIPM algorithm, but also reduces the dimensionality of the SDP problem. At the same time, in the construction of the new single snapshot observation vector, the small eigenvalues of the covariance matrix are discarded. The corresponding part can effectively suppress the influence of noise on the subsequent DOA parameter recovery process, and further improves the estimation accuracy of the algorithm. The simulation experiment also verifies the superiority of M-FIPM in terms of estimation accuracy and computing time.

Key words: atomic norm minimization, semi-definite programming (SDP), off-grid direction of arrival (DOA) estimation algorithm, fast interior point method (FIPM)

中图分类号:

TN911

陈涛, 史林, 申梦雨. 基于M-FIPM的无网格DOA估计算法[J]. 系统工程与电子技术, 2022, 44(2): 427-433.

Tao CHEN, Lin SHI, Mengyu SHEN. Gridless DOA estimation algorithm based on M-FIPM[J]. Systems Engineering and Electronics, 2022, 44(2): 427-433.

图/表 5

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