针对宽频段欠定波达方向估计问题，提出一种基于连续稀疏重构的波达方向估计方法.首先利用方向波数对互质阵列接收数据进行降维处理，接着对协方差矩阵向量化提高自由度；然后利用方向波数的空间稀疏性建立连续稀疏模型，通过求解相应的凸优化问题及多项式求根得到方向波数的高精度估计；最后结合Capon波束方法的思想实现频率和方向波数的配对.该方法有效避免了传统稀疏重构算法中由于角度域离散化所导致的模型失配对估计性能的影响，提高了估计精度和分辨力，可估计信号个数要大于实际阵元数.理论分析与仿真验证了本方法的正确性与有效性.
For the problem of broadband underdetermined direction of arrival (DOA) estimation, a novel DOA estimation algorithm is proposed based on the continuous sparse recovery. Firstly, the dimension of coprime array receiving data is reduced by using direction wavenumber and the covariance matrix is vectorized to improve the degree of freedom. Then, the continuous sparse recovery model of direction wavenumber is established using the spatial sparseness of direction wavenumber, and the estimation of direction wavenumber is achieved with convex optimization and polynomial rooting. Finally, the signal frequencies and direction wavenumbers are pair matched by using Capon method. With this method, offgrid effects caused by discretizing this range onto a grid in traditional sparse recovery can be neglected, it also improves accuracy and resolution of DOA estimation and the number of sources estimated by the proposed algorithm is larger than the number of actual arrays. Theoretical analysis and simulations demonstrate the effectiveness and feasibility of the proposed method.
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