A Bayesian Stochastic Machine for Sound Source Localization

Abstract

Abstract-Compared to conventional processors, stochastic computing architectures have strong potential to speed up computation time and to reduce power consumption. We present such an architecture, called Bayesian Machine (BM), dedicated to solving Bayesian inference problems. Given a set of noisy signals provided by low-level sensors, a BM estimates the posterior probability distribution of an unknown target information. In the present study, a BM is used to solve a sound source localization (SSL) problem: the BM computes the probability distribution of the position of a sound source given acoustic signals captured by a set of microphones. Assuming free field wave propagation (no reverberations), we express the SSL problem as the maximization of a likelihood function fed with audio features provided by the time-frequency (TF) analysis of the captured audio waves. The proposed BM uses bitwise parallel sampling to fuse the resulting multi-channel information. As the number of channels to fuse is large, the standard BM architecture encounters the so-called "time dilution problem" (long delays are necessary to obtain valid samples). We tackle this problem by using max-normalization of the distributions combined with a periodic re-sampling of the bit streams after processing a reasonably small subset of evidences. Finally, we compare the localization performance of the proposed machine with the results obtained using a standard version of the machine. The re-sampling leads to an impressive acceleration factor of 10 3 in the computation.

A Cognitive Stochastic Machine Based on Bayesian Inference: A Behavioral Analysis

“…The BMs were originally introduced in [5]. Later, in [10], the BM was adapted for Sound Source Localization (SSL) purposes. For more details, please refer to the mentioned articles.…”

“…This problem is called the temporal dilution. To speed up the time needed to compute the temporal dilution, a more enhanced version of the BM was introduced in [10], named the Sliced-BM.…”

“…The basic concept of Bayesian machines was presented in [5] and studies showed the robustness of the machine [4]. After dealing with simple examples of application, the Bayesian machine was adapted for SSL was presented in [10]. This introduced a new architecture, which is an extension of the standard version of the BM (Bayesian Machine), named the Sliced-BM.…”

“…Architecture of a Sliced-BM with 2 slices of q = n/2 columns each and 1 re-sampling unit between them. Originally published in[10] …”

Bayesian time-domain multiple sound source localization for a stochastic machine

“…Mono-source localization with a stochastic machine applied to signals pre-processed in the time-frequency (TF) domain was presented in [8] and deeply analyzed in [7]. However, one keypoint of stochastic machines is that they should avoid as much as possible signal pre-processing and focus directly on the Bayesian inference process.…”