基于矩阵填充的互质阵列欠定DOA估计方法

为了解决现有基于互质阵列的DOA估计方法舍弃差联合阵列中非均匀虚拟阵元而导致最大可估计信号数损失的问题，提出了一种基于矩阵填充的DOA估计方法。首先，根据差联合阵列与波程差一一对应的特性，构造一个部分元素缺失的Toeplitz化的阵列协方差矩阵，建立了基于矩阵填充的DOA估计模型，并验证了该模型满足零空间性质；然后，根据低秩矩阵填充理论，将DOA估计问题转化为矩阵核范数最小化问题进行求解，通过不定点延续算法将该协方差矩阵中的零元素进行填充恢复为完整协方差矩阵；最后，对协方差矩阵进行奇异值分解，转化为多项式求根，得到DOA的估计。仿真实验结果验证了本文方法的有效性和优越性。实验结果表明，本文方法能够对差联合阵列中的空洞部分进行有效填充，增加了可利用的阵列自由度，提高了可估计信号数，同时能够有效避免传统稀疏重构算法中由于角度域离散化导致的基不匹配问题对估计性能的影响，提高了估计精度和分辨力。

Underdetermined Direction of Arrival Estimation with Coprime Array Based on Matrix Completion

In the existing DOA estimation methods based on coprime array,discarding the non-uniform virtual elements in the difference coarray leads to the decrease of the number of the resolvable sources.In order to solve the problem,a DOA estimation method based on matrix completion was proposed.Firstly,according to the correspondence between the difference coarray and the wave path difference,a Toeplitz array covariance matrix was constructed,of which some elements are zero.Additionally,the DOA estimation model was established based on matrix completion and it was proved that the proposed model satisfied null space property.Secondly,according to the low rank matrix completion theory,the DOA estimation was transformed into the minimization of the nuclear norm,and then the Toeplitz matrix was recovered to the full covariance matrix by the fixed-point iterative algorithm.Finally,the DOA estimation was transformed into the determination of polynomial roots by singular value decomposition on the Toeplitz matrix.Simulation results showed the effectiveness and superiority of the proposed method.The experimental results showed that it can effectively fill the holes of the difference coarray,increase the available DOFs and the number of the resolvable signals.Meanwhile,it can eliminate the influence of the basis mismatch on the estimation performance in traditional sparse reconstruction methods due to the discretization in angel domain.Compared with the existing methods,the proposed method improved the DOA estimation accuracy and resolution.