# Tracking Multiple Audio Sources with the von Mises Distribution and Variational EM

## TL;DR

This paper introduces a novel variational EM approach for tracking multiple moving audio sources using the von Mises distribution, enabling efficient and accurate source trajectory estimation in dynamic environments.

## Contribution

It proposes a Bayesian filtering framework with a variational approximation for circular data, and introduces a new source birth method for improved initialization and detection.

## Key findings

- Effective tracking of moving sources demonstrated on LOCATA dataset.
- The variational EM algorithm is computationally efficient and accurate.
- The source birth method improves detection and trajectory estimation.

## Abstract

In this paper we address the problem of simultaneously tracking several moving audio sources, namely the problem of estimating source trajectories from a sequence of observed features. We propose to use the von Mises distribution to model audio-source directions of arrival with circular random variables. This leads to a Bayesian filtering formulation which is intractable because of the combinatorial explosion of associating observed variables with latent variables, over time. We propose a variational approximation of the filtering distribution. We infer a variational expectation-maximization algorithm that is both computationally tractable and time efficient. We propose an audio-source birth method that favors smooth source trajectories and which is used both to initialize the number of active sources and to detect new sources. We perform experiments with the recently released LOCATA dataset comprising two moving sources and a moving microphone array mounted onto a robot.