Maximum Likelihood-Based Gridless DoA Estimation Using Structured Covariance Matrix Recovery and SBL With Grid Refinement
Maximum Likelihood-Based Gridless DoA Estimation Using Structured Covariance Matrix Recovery and SBL With Grid Refinement
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DOI：
10.1109/tsp.2023.3254919
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发表时间：
2023-01-01
影响因子：
5.4
通讯作者：
Rao, Bhaskar D.
中科院分区：
文献类型：
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作者：
Pote, Rohan R.;Rao, Bhaskar D.
我们考虑在线谱或波达方向估计等应用中使用的参数测量模型，其目标是以无网格的方式估计底层参数。我们将重点放在随机最大似然估计(MLE)框架上，并通过对目标的重新参数化和利用稀疏贝叶斯学习(SBL)方法来克服过去模型的复杂性。SBL被证明是一种相关性感知方法，对于潜在问题，是一种基于网格的技术，用于恢复测量的结构化协方差矩阵。对于测量是规则间隔的空间(或时间)样本的情况，结构化矩阵可表示为采样的Toeplitz矩阵。在这种情况下，SBL目标的附加约束和重新参数化导致了提出的基于最大似然估计的结构化矩阵恢复技术。该优化问题是一个非凸优化问题，提出了一种基于优化最小化的迭代过程来估计结构矩阵，每次迭代求解一个半定规划。借助于Caratheodory-Fejer关于半正定Toeplitz矩阵分解的结果，我们以无网格的方式恢复感兴趣的参数。对于不规则间隔样本的一般情况，我们提出了一种迭代SBL过程，该过程细化网格点以提高潜在震源位置附近的分辨率，同时保持较低的每次迭代复杂度。我们给出了数值结果，比较了所提出的技术与其他无网格技术的性能，以及Cramer-Rao界。提出的相关性感知方法对快照较少、相关或紧密分离的信源等问题具有更强的健壮性，并提高了信源的可识别性。
We consider the parametric measurement model employed in applications such as line spectral or direction-of-arrival estimation with the goal to estimate the underlying parameter in a gridless manner. We focus on the stochastic maximum likelihood estimation (MLE) framework and overcome the model complexities of the past by reparameterization of the objective and exploiting the sparse Bayesian learning (SBL) approach. SBL is shown to be a correlation-aware method and, for the underlying problem, a grid-based technique for recovering a structured covariance matrix of the measurements. For the case when measurements are spatial (or temporal) samples at regular intervals, the structured matrix is expressible as a sampled Toeplitz matrix. In this case, additional constraints and reparameterization of the SBL objective leads to the proposed structured matrix recovery technique based on MLE. The optimization problem is non-convex and a majorization-minimization based iterative procedure is proposed to estimate the structured matrix; each iteration solves a semidefinite program. We recover the parameter of interest in a gridless manner by appealing to the Caratheodory-Fejer result on decomposition of positive semidefinite Toeplitz matrices. For the general case of irregularly spaced samples, we propose an iterative SBL procedure that refines grid points to increase resolution near potential source locations, while maintaining a low per iteration complexity. We provide numerical results to compare the performance of the proposed techniques with other gridless techniques, and the Cramer-Rao bound. The proposed correlation-aware approach is more robust to issues such as fewer snapshots, correlated or closely separated sources, and improves sources identifiability.