No abstract

The reconstruction of sound sources by using inverse methods is known to be prone to estimation errors due to measurement noise, model mismatch, and poor conditioning of the inverse problem. This paper introduces a solution to map the estimation errors together with the reconstructed sound sources. From a Bayesian perspective, it initializes a Gibbs sampler with the Bayesian focusing method. The proposed Gibbs sampler is shown to converge within a few iterations, which makes it realistic for practical purposes. It also turns out to be very flexible in various scenarios. One peculiarity is the capability to directly operate on the cross-spectral matrix. Another one is to easily accommodate sparse priors. Eventually, it can also account for uncertainties in the microphone positions, which reinforces the regularization of the inverse problem.

The characterization of acoustic sources typically involves the retro-propagation of the acoustic field measured with a microphone array to a mesh of the surface of interest, which amounts to solve an inverse problem. Such an inverse problem is built on the basis of a forward model prone to uncertainties arising from mismatches with the physics of the experiment. Assessing the effects of these unavoidable uncertainties on the resolution of the inverse problem represents a challenge. The present paper introduces a practical solution to measure these effects by conducting a sensitivity analysis. The latter provides a mean to identify and rank the main sources of uncertainty through the estimation of sensitivity indices. Two inverse methods are investigated through the sensitivity analysis: Beamforming and Bayesian focusing. The propagation of uncertainties is carried on numerically. The consistency between the real experiment and its numerical simulation is assessed by means of a small batch of measurements performed in a semi-anechoic chamber.

For the characterization of acoustic sources, a common approach is to retropropagate the sound pressure measured with a microphone array, which is often performed through the resolution of an inverse problem. The ill-posed nature of this problem, as well as the limited number of measurements, are known to reduce the quality of the source reconstruction. A practical solution to these limitations is to increase the number of measurements with new array placements. However, finding the best array positions is not a straightforward process. The present paper tackles this issue by introducing a sequential approach that select at each iteration the optimal array placement. The proposed approach builds on two features rooted in a Bayesian framework: an inverse method called "Bayesian focusing" and a Bayesian search criterion based on the Kullback-Leibler divergence. Simulations results for the characterization of a directive source are used to illustrate the performance of the proposed approach. It is shown that for a fixed number of iterations, the proposed approach performs better than ones where the successive placements are randomly selected around the source, or others where the placements follow a deterministic spherical grid pattern.

Source localization and quantification by an acoustic array of microphones depend to a great extent on an accurate knowledge of the antenna position towards the radiating device. The present work details a methodology to determine the location of the microphones in relation to an object of study, starting from its geometric shape and that of the array, in order to reproduce an experimental configuration in any retro-propagating method. A set of reference sources are placed on several prominent locations of the device to estimate the times of flight (ToF) (and distances) between them and the microphones, connecting the array and the object together. The overall geometric configuration is thus defined by an Euclidean Distance Matrix (EDM), which is basically the matrix of squared distances between points. First, MultiDimensional Unfolding (MDU) technique is used to reconstruct the point set from distances. Second, this point set is then aligned with the device, using reference sources as anchor nodes. This orthogonal Procustes problem is solved by the Kabsch algorithm to obtain the optimal rotation and translation matrices between the coordinate system of the array and that of the object of study. The methodology is detailed, validated first by a numerical simulation of a typical experimental set-up. An experimental campaign is finally carried out to assess the robustness of the method in a typical test case.