Abstract This paper provides a method to solve off-grid direction-of-arrival (DOA) estimation for nonuniform linear array (NLA) correlated source condition through hierarchical sparse recovery and asymptotic minimum variance (AMV) criterion. In this method, space is firstly divided into a discretized grid. Most rows and columns of the signal covariance matrix modeled on this grid are zero vectors because the number of sources is considerably smaller than that of grid points. Hence, the vectorized signal covariance matrix is regarded as a block-sparse vector, and active blocks are sparse vectors. Based on this, a hierarchical sparse prior is then assigned on the vectorized signal covariance matrix to encourage the sparsity between and within blocks. Finally, the variational Bayesian inference is applied to estimate the vectorized signal covariance matrix. Furthermore, first-order Taylor series expansion is applied to approximate the steering vector as a function of the grid error between the true DOA and the closest grid point. Grid error is estimated under the AMV criterion and applied to modify the grid iteratively, thus alleviating the basis mismatch. Simulation results show that the proposed method achieves high estimation accuracy for the NLA correlated source condition.

中文翻译：

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通过贝叶斯框架中的分层稀疏恢复和渐近最小方差准则对非均匀线性阵列相关源的离网 DOA 估计

摘要 本文提供了一种通过分层稀疏恢复和渐近最小方差（AMV）准则解决非均匀线阵（NLA）相关源条件下离网到达方向（DOA）估计的方法。在该方法中，首先将空间划分为离散化的网格。在这个网格上建模的信号协方差矩阵的大多数行和列都是零向量，因为源的数量远小于网格点的数量。因此，向量化的信号协方差矩阵被视为块稀疏向量，活动块是稀疏向量。基于此，然后在矢量化信号协方差矩阵上分配分层稀疏先验以促进块之间和块内的稀疏性。最后，应用变分贝叶斯推理来估计矢量化信号协方差矩阵。此外，应用一阶泰勒级数展开来近似作为真实 DOA 和最近网格点之间的网格误差的函数的导向向量。在 AMV 准则下估计网格误差并应用于迭代修改网格，从而减轻基础失配。仿真结果表明，该方法对NLA相关源条件具有较高的估计精度。