Sparse arrays are special geometrical arrangements of sensors which overcome some of the drawbacks associated with dense uniform arrays and require fewer sensors. For direction finding applications, sparse arrays with the same number of sensors can resolve more sources while providing higher resolution than a dense uniform array. This has been verified numerically and with real data for one-dimensional microphone arrays. In this study the use of nested and co-prime arrays is examined with sparse Bayesian learning (SBL), which is a compressive sensing algorithm, for estimating sparse vectors and support. SBL is an iterative parameter estimation method and can process multiple snapshots as well as multiple frequency data within its Bayesian framework. A multi-frequency variant of SBL is proposed, which accounts for non-flat frequency spectra of the sources. Experimental validation of azimuth and elevation [two-dimensional (2D)] direction-of-arrival (DOA)estimation are provided using sparse arrays and real data acquired in an anechoic chamber with a rectangular array. Both co-prime and nested arrays are obtained by sampling this rectangular array. The SBL method is compared with conventional beamforming and multiple signal classification for 2D DOA estimation of experimental data.

中文翻译：

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使用实验数据的方位角和仰角的稀疏平面阵列

稀疏阵列是传感器的特殊几何结构，它克服了与密集均匀阵列相关的一些缺点，并且需要更少的传感器。对于测向应用，与密集均匀阵列相比，具有相同数量传感器的稀疏阵列可以解析更多源，同时提供更高的分辨率。对于一维麦克风阵列，已经用数字和真实数据对此进行了验证。在这项研究中，通过稀疏贝叶斯学习（SBL）（一种压缩感知算法）来研究嵌套数组和互素数组的使用，以估计稀疏矢量和支持。SBL是一种迭代参数估计方法，可以在其贝叶斯框架内处理多个快照以及多个频率数据。提出了SBL的多频变体，这说明了源的非平坦频谱。使用稀疏阵列和在带有矩形阵列的消声室中获取的实际数据，提供了方位角和仰角[二维（2D）]到达方向（DOA）估计的实验验证。通过对该矩形数组进行采样，可以获得互素数组和嵌套数组。将SBL方法与常规波束成形和多信号分类进行比较，以对实验数据进行2D DOA估计。