Sound source localization in a randomly inhomogeneous medium using matched statistical moment method

This paper investigates the problem of sound source localization from acoustical measurements obtained by an array of microphones. The sound propagation medium is assumed to be randomly inhomogeneous, being modelled by a random function of space. In this case, classical source localization methods (e.g., beamforming, near-field acoustical holography, and time reversal) cannot be used anymore. Therefore, an approach based on the statistical moments of acoustical measurement is proposed to solve the aforementioned problem. In this work, a Karhunen-Loève expansion is used so that the random medium can be represented by a small number of uncorrelated and identically distributed random variables. The statistical characteristics of the measurements in terms of probability density function and statistical moments are also studied. Then, the sound source is localized by minimizing the error of statistical moments between the real measurements obtained from the microphone array and the measurements simulated from an assumed source. Finally, a numerical example is introduced to justify the proposed method. This experiment shows that the random field can be replicated by a very small number of random variables, the statistical moments of measurements guarantee the convergence, and the source location can be accurately estimated using the proposed source localization method.