基于Toeplitz协方差矩阵重构的互质阵列DOA估计方法

Direction of Arrival Estimation with Coprime Array Based on Toeplitz Covariance Matrix Reconstruction

针对基于互质阵列的欠定DOA估计方法对于虚拟阵元非连续部分利用率不高的问题,该文提出一种基于Toeplitz协方差矩阵重构的DOA估计方法。首先,从互质阵列差联合阵的角度分析虚拟阵元分布特性,结合其与协方差矩阵中各元素得到的波程差存在对应关系,将协方差矩阵进行扩展得到一个数据缺失的高维协方差矩阵;然后,根据矩阵填充理论,用迹范数代替秩范数进行松弛,对缺失元素进行填充;最后,利用现有root-MUSIC方法进行DOA估计。理论分析和仿真结果表明,该方法提升了虚拟阵元的利用率,从而增加了虚拟孔径和可估计信号数,同时无需对角度域进行离散化处理,有效消除了模型失配的影响,并且避免了正则化参数选取问题,提高了估计精度和分辨率。

In order to improve the utilization of non-contiguous virtual array elements in the underdetermined DOA estimation of the coprime array, a DOA estimation method based on Toeplitz covariance matrix reconstruction is proposed. First, the virtual array element distribution characteristics of the matrix are analyzed from the perspective of the difference coarray. Additionally, according to the correspondence between the difference coarray and the wave path difference, the covariance matrix is extended to a Toeplitz array covariance matrix, of which some elements are zero. Then, the Toeplitz matrix is recovered to the full covariance matrix according to the low rank matrix completion theory. Finally, the root-MUSIC method is employed for the DOA estimation. Theoretical analysis and simulation results show that this method can increase the number of the resolvable signals by increasing the number of virtual array elements, eliminate the effect of the off-grid effect without discretization of the angle domain, and avoid regularization parameter selection. Therefore, the estimation accuracy and resolution are improved.