A Bayesian direction-of-arrival model for an undetermined number of sources using a two-microphone array

Moving sound source localization and tracking for an autonomous robot equipped with a self-rotating bi-microphone array

In this paper, we present two approaches to localizing and tracking a sound source that moves in a three-dimensional (3D) space. The sound signal was captured by a unique bi-microphone system that rotates at a constant angular velocity. The motion of the sound source along with the rotation of the bi-microphone array produces a sinusoidal inter-channel distance difference (ICDD) signal with time-varying amplitude and phase. Four state-space models were developed and employed to design extended Kalman filters (EKFs) that identify instantaneous amplitude and phase of the ICDD signal. Both theoretical and numerical observability analyses of the four state-space models were performed to reveal singularities of the proposed EKFs in the domain of interest. We also developed a Hilbert-transform based method that localizes the sound source by comparing the true analytic ICDD signal to a virtual reference signal with zero elevation and azimuth angles. A moving average filter is then applied to reduce the noise and the effect of the artifacts at the beginning and the ending portions of the estimates. The effectiveness of the proposed methods was evaluated using comparison studies in simulation.

Fast grid-free strength mapping of multiple sound sources from microphone array data using a Transformer architecture

Conventional microphone array methods for the characterization of sound sources that require a focus-grid are, depending on the grid resolution, either computationally demanding or limited in reconstruction accuracy. This paper presents a deep learning method for grid-free source characterization using a Transformer architecture that is exclusively trained with simulated data. Unlike previous grid-free model architectures, the presented approach requires a single model to characterize an unknown number of ground-truth sources. The model predicts a set of source components, spatially arranged in clusters. Integration over the predicted cluster components allows for the determination of the strength for each ground-truth source individually. Fast and accurate source mapping performance of up to ten sources at different frequencies is demonstrated and strategies to reduce the training effort at neighboring frequencies are given. A comparison with the established grid-based CLEAN-SC and a probabilistic sparse Bayesian learning method on experimental data emphasizes the validity of the approach.

A survey of sound source localization with deep learning methods

This article is a survey of deep learning methods for single and multiple sound source localization, with a focus on sound source localization in indoor environments, where reverberation and diffuse noise are present. We provide an extensive topography of the neural network-based sound source localization literature in this context, organized according to the neural network architecture, the type of input features, the output strategy (classification or regression), the types of data used for model training and evaluation, and the model training strategy. Tables summarizing the literature survey are provided at the end of the paper, allowing a quick search of methods with a given set of target characteristics.

Deep learning assisted sound source localization using two orthogonal first-order differential microphone arrays

Sound source localization in noisy and reverberant rooms using microphone arrays remains a challenging task, especially for small-sized arrays. Recent years have seen promising advances on deep learning assisted approaches by reformulating the sound localization problem as a classification one. A key to the deep learning-based approaches lies in extracting sound location features effectively in noisy and reverberant conditions. The popularly adopted features are based on the well-established generalized cross correlation phase transform (GCC-PHAT), which is known to be helpful in combating room reverberation. However, the GCC-PHAT features may not be applicable to small-sized arrays. This paper proposes a deep learning assisted sound localization method using a small-sized microphone array constructed by two orthogonal first-order differential microphone arrays. An improved feature extraction scheme based on sound intensity estimation is also proposed by decoupling the correlation between sound pressure and particle velocity components in the whitening weighting construction to enhance the robustness of the time-frequency bin-wise sound intensity features. Simulation and real-world experimental results show that the proposed deep learning assisted approach can achieve higher spatial resolution and is superior to its state-of-the-art counterparts using the GCC-PHAT or sound intensity features for small-sized arrays in noisy and reverberant environments.

Model-based Bayesian analysis in acoustics-A tutorial

Bayesian analysis has been increasingly applied in many acoustical applications. In these applications, prediction models are often involved to better understand the process under investigation by purposely learning from the experimental observations. When involving the model-based data analysis within a Bayesian framework, issues related to incorporating the experimental data and assigning probabilities into the inferential learning procedure need fundamental consideration. This paper introduces Bayesian probability theory on a tutorial level, including fundamental rules for manipulating the probabilities, and the principle of maximum entropy for assignment of necessary probabilities prior to the data analysis. This paper also employs a number of examples recently published in this journal to explain detailed steps on how to apply the model-based Bayesian inference to solving acoustical problems.

Model-based Bayesian direction of arrival analysis for sound sources using a spherical microphone array

In many room acoustics and noise control applications, it is often challenging to determine the directions of arrival (DoAs) of incoming sound sources. This work seeks to solve this problem reliably by beamforming, or spatially filtering, incoming sound data with a spherical microphone array via a probabilistic method. When estimating the DoA, the signal under consideration may contain one or multiple concurrent sound sources originating from different directions. This leads to a two-tiered challenge of first identifying the correct number of sources, followed by determining the directional information of each source. To this end, a probabilistic method of model-based Bayesian analysis is leveraged. This entails generating analytic models of the experimental data, individually defined by a specific number of sound sources and their locations in physical space, and evaluating each model to fit the measured data. Through this process, the number of sources is first estimated, and then the DoA information of those sources is extracted from the model that is the most concise to fit the experimental data. This paper will present the analytic models, the Bayesian formulation, and preliminary results to demonstrate the potential usefulness of this model-based Bayesian analysis for complex noise environments with potentially multiple concurrent sources.

A Bayesian spherical harmonics source radiation model for sound field control

In sound field reproduction and sound field control systems, the acoustic transfer functions between a set of sources and an extended reproduction area need to be accurately estimated in order to achieve good performance. This implies that large amounts of measurements should be performed if the area is large compared to the wavelengths of interest. In this paper, a method for reconstructing these transfer functions in highly damped conditions is proposed by using only a small number of measurements in the reproduction area. The source radiation is modeled with the spherical harmonics basis and its amplitude coefficients are fitted with Bayesian inference. This approach is validated in a sound field control experiment where a set of 12 control loudspeakers attenuate the sound pressure level generated by a set of six primary loudspeakers in a quiet zone while minimizing their radiation into a listening zone. The performance of the approach is studied by analyzing the sound field reconstruction and the sound field control performance. It is shown that it is possible to get-with few measurements and the source radiation model-results similar to those achieved using a dense grid of transfer function measurements.

Bayesian Inference for Acoustic Direction of Arrival Analysis Using Spherical Harmonics

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.

Bayesian acoustic analysis of multilayer porous media

In many acoustical applications, porous materials may be stratified or physically anisotropic along their depth direction. In order to better understand the sound absorbing mechanisms of these porous media, the depth-dependent anisotropy can be approximated as a multilayer combination of finite-thickness porous materials with each layer being considered as isotropic. The uniqueness of this work is that it applies Bayesian probabilistic inference to determine the number of constituent layers in a multilayer porous specimen and macroscopic properties of their pores. This is achieved through measurement of the acoustic surface impedance and subsequent transfer-matrix analysis based on a valid theoretical model for the acoustical properties of porous media. The number of layers considered in the transfer-matrix analysis is varied, and Bayesian model selection is applied to identify individual layers present in the porous specimen and infer the parameters of their microstructure. Nested sampling is employed in this process to solve the computationally intensive inversion problem.

A model-based Bayesian framework for sound source enumeration and direction of arrival estimation using a coprime microphone array

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.

Room acoustic modal analysis using Bayesian inference

Strong modal behavior can produce undesirable acoustical effects, particularly in recording studios and other small rooms. Although closed-form solutions exist to predict modes in rectangular rooms with parallel walls, such solutions are typically not available for rooms with even modest geometrical complexity. This work explores a method to identify multiple decaying modes in experimentally measured impulse responses from existing spaces. The method adopts a Bayesian approach working in the time domain to identify numerous decaying modes in an impulse response. Bayesian analysis provides a unified framework for two levels of inference: model selection and parameter estimation. In this context model selection determines the number of modes present in an impulse response, while parameter estimation determines the relevant parameters (e.g., decay time and frequency) of each mode. The Bayesian analysis in this work is implemented using an approximate numerical technique called nested sampling. Experimental measurements are performed in a test chamber in two different configurations. Experimentally measured results are compared with simulated values from the Bayesian analyses along with other, more classical calculations. Discussion of the results and the applicability of the method is provided.

Investigations on sound energy decays and flows in a monumental mosque

This work investigates the sound energy decays and flows in the Süleymaniye Mosque in İstanbul. This is a single-space superstructure having multiple domes. The study searches for the non-exponential sound energy decay characteristics. The effect of different material surfaces and volumetric contributions are investigated using acoustic simulations and in situ acoustical measurements. Sound energy decay rates are estimated by Bayesian decay analysis. The measured data reveal double- or triple-slope energy decay profiles within the superstructure. To shed light on the mechanism of energy exchanges resulting in multi-slope decay, spatial sound energy distributions and energy flow vectors are studied by diffusion equation model (DEM) simulations. The resulting sound energy flow vector maps highlight the contribution of a sound-reflective central dome contrasted with an absorptive carpeted floor in providing delayed energy feedback. In contrast, no multi-slope energy decay pattern is observed in DEM simulations with a bare marble floor, which generates a much more diffuse sound field than in the real situation with a carpeted floor. The results demonstrate that energy fragmentation, in support of the non-exponential energy decay profile, is due to both the sound absorption characteristics of materials and to their distributions, as well as to relations between the subvolumes of the mosque's interior.

Broadband implementation of coprime linear microphone arrays for direction of arrival estimation

Coprime arrays represent a form of sparse sensing which can achieve narrow beams using relatively few elements, exceeding the spatial Nyquist sampling limit. The purpose of this paper is to expand on and experimentally validate coprime array theory in an acoustic implementation. Two nested sparse uniform linear subarrays with coprime number of elements ( M and N) each produce grating lobes that overlap with one another completely in just one direction. When the subarray outputs are combined it is possible to retain the shared beam while mostly canceling the other superfluous grating lobes. In this way a small number of microphones ( N+M-1) creates a narrow beam at higher frequencies, comparable to a densely populated uniform linear array of MN microphones. In this work beampatterns are simulated for a range of single frequencies, as well as bands of frequencies. Narrowband experimental beampatterns are shown to correspond with simulated results even at frequencies other than the arrays design frequency. Narrowband side lobe locations are shown to correspond to the theoretical values. Side lobes in the directional pattern are mitigated by increasing bandwidth of analyzed signals. Direction of arrival estimation is also implemented for two simultaneous noise sources in a free field condition.

Experimental validation of a coprime linear microphone array for high-resolution direction-of-arrival measurements

Coprime linear microphone arrays allow for narrower beams with fewer sensors. A coprime microphone array consists of two staggered uniform linear subarrays with M and N microphones, where M and N are coprime with each other. By applying spatial filtering to both subarrays and combining their outputs, M+N-1 microphones yield M⋅N directional bands. In this work, the coprime sampling theory is implemented in the form of a linear microphone array of 16 elements with coprime numbers of 9 and 8. This coprime microphone array is experimentally tested to validate the coprime array theory. Both predicted and measured results are discussed. Experimental results confirm that narrow beampatterns as predicted by the coprime sampling theory can be obtained by the coprime microphone array.