Xiang Ning, Landschoot Christopher
Graduate Program in Architectural Acoustics, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
Entropy (Basel). 2019 Jun 10;21(6):579. doi: 10.3390/e21060579.
This work applies two levels of inference within a Bayesian framework to accomplish estimation of the directions of arrivals (DoAs) of sound sources. The sensing modality is a spherical microphone array based on spherical harmonics beamforming. When estimating the DoA, the acoustic signals may potentially contain one or multiple simultaneous sources. Using two levels of Bayesian inference, this work begins by estimating the correct number of sources via the higher level of inference, Bayesian model selection. It is followed by estimating the directional information of each source via the lower level of inference, Bayesian parameter estimation. This work formulates signal models using spherical harmonic beamforming that encodes the prior information on the sensor arrays in the form of analytical models with an unknown number of sound sources, and their locations. Available information on differences between the model and the sound signals as well as prior information on directions of arrivals are incorporated based on the principle of the maximum entropy. Two and three simultaneous sound sources have been experimentally tested without prior information on the number of sources. Bayesian inference provides unambiguous estimation on correct numbers of sources followed by the DoA estimations for each individual sound sources. This paper presents the Bayesian formulation, and analysis results to demonstrate the potential usefulness of the model-based Bayesian inference for complex acoustic environments with potentially multiple simultaneous sources.
这项工作在贝叶斯框架内应用了两个层次的推理来完成声源到达方向（DoA）的估计。传感模式是基于球谐波束形成的球形麦克风阵列。在估计DoA时，声学信号可能潜在地包含一个或多个同时存在的声源。利用两个层次的贝叶斯推理，这项工作首先通过较高层次的推理，即贝叶斯模型选择，来估计声源的正确数量。接着通过较低层次的推理，即贝叶斯参数估计，来估计每个声源的方向信息。这项工作使用球谐波束形成来制定信号模型，该模型以具有未知数量声源及其位置的解析模型的形式对传感器阵列上的先验信息进行编码。基于最大熵原理，纳入了模型与声音信号之间差异的可用信息以及到达方向的先验信息。在没有关于声源数量的先验信息的情况下，对两个和三个同时存在的声源进行了实验测试。贝叶斯推理对声源的正确数量提供了明确的估计，随后对每个单独声源进行了DoA估计。本文给出了贝叶斯公式和分析结果，以证明基于模型的贝叶斯推理在具有潜在多个同时声源的复杂声学环境中的潜在有用性。
