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针对稀疏分解方法进行均匀圆阵(UCA)的二维波达方向(DOA)估计运算复杂度大的问题,提出了一种基于协方差矩阵高阶幂稀疏分解的二维DOA估计新算法。该算法首先利用协方差矩阵高阶幂无需进行特征值分解和信源数估计的特性,构建了协方差矩阵高阶幂的稀疏分解向量;然后运用粒度分层思想,构造了粗区域估计和细方位估计的分层多粒度的快速分解模型,分层字典的长度大大减少,在保持估计精度的前提下,算法运算时间远小于现有的恒定冗余字典的稀疏分解方法,从而解决了基于稀疏分解的圆阵二维DOA估计问题。论文提出的算法与二维MUSIC算法相比,估计精度高,且能满足对相干信号的估计。仿真结果验证了算法的有效性和可行性。
In order to solve the problem of computational complexity of two-dimensional DOA estimation for uniform circular array (UCA) based on sparse decomposition, a new two-dimensional DOA estimation algorithm based on high-order sparse decomposition of covariance matrix is proposed. Firstly, the covariance matrix high-order power is used to construct the sparse decomposition vector of higher-order covariance matrices without eigenvalue decomposition and source number estimation. Then, by using granularity stratification theory, the rough area estimation and the fine Azimuth estimation of hierarchical multi-granularity of the rapid decomposition model, the length of the hierarchical dictionary is greatly reduced, while maintaining the accuracy of the premise, the algorithm operation time is much smaller than the existing constant redundant dictionary sparse decomposition method to solve the sparse Discrete circular array DOA estimation problem. Compared with two-dimensional MUSIC algorithm, the proposed algorithm has high estimation accuracy and can satisfy the estimation of coherent signals. Simulation results verify the effectiveness and feasibility of the algorithm.