Bush Dane, Xiang Ning
Graduate Program in Architectural Acoustics School of Architecture, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
J Acoust Soc Am. 2018 Jun;143(6):3934. doi: 10.1121/1.5042162.
Coprime microphone arrays use sparse sensing to achieve greater degrees of freedom, while the coprimality of the microphone subarrays help resolve grating lobe ambiguities. The result is a narrow beam at frequencies higher than the spatial Nyquist limit allows, with residual side lobes arising from aliasing. These side lobes can be mitigated when observing broadband sources, as shown by Bush and Xiang [J. Acoust. Soc. Am. 138, 447-456 (2015)]. Peak positions may indicate directions of arrival in this case; however, one must first ask how many sources are present. In answering this question, this work employs a model describing scenes with potentially multiple concurrent sound sources. Bayesian inference is used to first select which model the data prefer from competing models before estimating model parameters, including the particular source locations. The model is a linear combination of Laplace distribution functions (one per sound source). The likelihood function is explored by a Markov Chain Monte Carlo method called nested sampling in order to evaluate Bayesian evidence for each model. These values increase monotonically with model complexity; however, diminished returns are penalized via an implementation of Occam's razor.
互质麦克风阵列利用稀疏传感来实现更高的自由度，而麦克风子阵列的互质性有助于解决栅瓣模糊问题。结果是在高于空间奈奎斯特极限所允许的频率处形成一个窄波束，同时由于混叠会产生残余旁瓣。正如布什和向[《美国声学学会杂志》138, 447 - 456 (2015)]所表明的，在观测宽带声源时，这些旁瓣可以得到缓解。在这种情况下，峰值位置可能指示到达方向；然而，首先必须要问存在多少个声源。为了回答这个问题，这项工作采用了一个描述可能存在多个并发声源场景的模型。在估计包括特定声源位置在内的模型参数之前，先使用贝叶斯推理从竞争模型中选择数据更倾向的模型。该模型是拉普拉斯分布函数的线性组合（每个声源一个）。通过一种名为嵌套采样的马尔可夫链蒙特卡罗方法来探索似然函数，以便评估每个模型的贝叶斯证据。这些值会随着模型复杂度单调增加；然而，通过实施奥卡姆剃刀原理，收益递减会受到惩罚。
