Two-dimensional wave field decomposition using circular microphone arrays and its application to acoustic source localization

Abstract

Two-dimensional wave fields can be used as reasonable models for propagating acoustic sound fields in closed rooms where ceiling and floor reflections are sufficiently attenuated. A natural way of analyzing a 2D wave field is to decompose it into an orthogonal set of eigensolutions to the acoustic wave equation in cylindrical coordinates, i.e., the cylindrical harmonics. These harmonics can be shown to be the coefficients of a Fourier series expansion applied along a circular aperture that is located within the 2D wave field under observation. Circular microphone arrays and, in particular, microphones mounted in a rigid cylindrical baffle that perform the cylindrical harmonics decomposition will be presented and its advantages and limitations will be discussed. As a specific example for utilizing the wave field decomposition approach, its application to acoustic source localization will be considered. By exploiting structural similarities between the response of linear microphone arrays and the decomposed response of circular microphone arrays, most well-known subspace tracking algorithms can be applied to this problem with only minor modifications. It will be shown that acoustic source localization based on wave field decomposition has the potential to track multiple simultaneously active sources in the array’s full 360° field of view.