Due to the rapid development and wide application of compressed sensing and sparse reconstruction theory, there exists a series of sparsity-based methods for the antenna sensor array direction of arrival (DOA) estimation with excellent performance. However, it is known that this kind of algorithms always suffers from the problem of grid mismatch. To overcome this shortcoming, a gridless DOA estimation algorithm with finite rate of innovation (FRI) based on a symmetric Toeplitz covariance matrix is proposed for uniform linear array (ULA) in this paper. In particular, a multiple measurement vector (MMV) FRI reconstruction model is built by exploiting the covariance data denoised according to covariance fitting criteria rather than the direct data or the original covariance data, which is commonly used in other representative gridless DOA estimation methods. Next, DOA can be retrieved from the recovered covariance matrix by utilizing an annihilating filter because each covariance data is a linear combination of complex exponentials. It guarantees to produce an exact spatial sparse estimate without discretization required by existing sparsity-based DOA estimation methods. Finally, the effectiveness and superiority of the proposed algorithm are demonstrated by numerical simulations.

由于压缩感知和稀疏重建理论的快速发展和广泛应用，存在一系列基于稀疏性的天线传感器阵列到达方向（DOA）估计方法，具有出色的性能。然而，已知这种算法总是遭受网格失配的问题。为了克服这一缺点，针对均匀线性阵列（ULA），提出了一种基于对称Toeplitz协方差矩阵的有限创新率（FRI）的无网格DOA估计算法。特别是，通过利用根据协方差拟合标准去噪的协方差数据而不是直接数据或原始协方差数据来构建多测量向量（MMV）FRI重建模型，在其他有代表性的无网格DOA估计方法中常用。接下来，由于每个协方差数据都是复指数的线性组合，因此可以通过使用filter灭滤波器从恢复的协方差矩阵中检索DOA。它保证产生精确的空间稀疏估计，而无需现有基于稀疏度的DOA估计方法所要求的离散化。最后，通过数值仿真证明了该算法的有效性和优越性。