Estimation of multiple sound sources with data and model uncertainties using the EM and evidential EM algorithms

• We use an expectation-maximization (EM) algorithm to estimate the multiple sound sources.
• We improve the model by considering two kinds of uncertainties in the sound propagation and measurement process and representing them using uncertain data.
• We use Evidential EM (E2M) algorithm to estimate multiple sound sources in the uncertain model.
• Both simulation and real experiments are shown to justify the advantage of using the EM in the case without uncertainty and the E2M in the uncertain model.

This paper considers the problem of identifying multiple sound sources from acoustical measurements obtained by an array of microphones. The problem is solved via maximum likelihood. In particular, an expectation-maximization (EM) approach is used to estimate the sound source locations and strengths, the pressure measured by a microphone being interpreted as a mixture of latent signals emitted by the sources. This work also considers two kinds of uncertainties pervading the sound propagation and measurement process: uncertain microphone locations and uncertain wavenumber. These uncertainties are transposed to the data in the belief functions framework. Then, the source locations and strengths can be estimated using a variant of the EM algorithm, known as the Evidential EM (E2M) algorithm. Eventually, both simulation and real experiments are shown to illustrate the advantage of using the EM in the case without uncertainty and the E2M in the case of uncertain measurement.