基于原子范数的互质阵列协方差矩阵重构算法

Covariance matrix reconstruction algorithm of coprime array based on minimum atomic norm

摘要:

针对互质阵列的虚拟阵列插值过程中协方差项的非均匀加权问题，将互质阵列协方差矩阵重构转换为低秩矩阵填充与原子范数重构，提出基于原子范数的互质阵列协方差矩阵重构算法。该算法先利用广义增广法得到非完备的互质阵列协方差矩阵，并利用截断的均值奇异值门限填充法得到虚拟阵列的协方差矩阵初值，然后对其进行原子范数最小化求解，实现稳健的正定Toeplitz协方差矩阵重构。该算法充分利用互质阵列协方差矩阵信息，有效提高互质阵列DOA估计算法的稳定性，降低计算复杂度。

Abstract:

Aiming at the nonuniform weighting for covariance lags in virtual array interpolation, the covariance matrix reconstruction of the coprime array is modeled as the low-rank matrix completion and atomic norm reconstruction. A novel covariance matrix reconstruction algorithm based on atomic norm for coprime array is proposed. Firstly, the Generalized Augmentation Approach(GAA) is utilized to obtain a partial covariance matrix of the coprime array. Then the partial covariance matrix is completed with the truncated mean singular value threshold method and reconstructed through the atomic norm minimization. A robust positive definite Toeplitz covariance matrix is accomplished. The proposed algorithm makes full use of the information contained in the coprime array to improve the stability of Direction of Arrival(DOA) estimation algorithm and reduce the computational complexity.