Combined microphone array for precise localization of sound source using the acoustic intensimetry

Abstract

Various applications require a compact system for acoustic source localization. Intensimetry methods based on three-dimensional (3D) acoustic intensity are favorable for miniaturizing localization array systems because of the small errors at low Helmholtz numbers. However, in practice, conventional 3D intensimetry has not performed well at high Helmholtz numbers because of large spatial and spectral bias errors. In this work, the spatial bias error of 3D acoustic intensimetry is analyzed with respect to the irregularities in directivity. The magnitude of spatial bias error is found to be proportional to the gradient of the array directional response. Therefore, the maximum spatial bias error occurs in the vicinity of the direction corresponding to the maximum or minimum value of the array directional response. For smoothing the spatial array directional response, a combination of array modules with mutual symmetry in directivity is proposed as a compensation method. A stellated octahedral shape, and its truncated form, can regularize the array directional response while maintaining a small number of microphones. Source localization is tested using single and combined modules. The root-mean-square error of the bearing angle when using the combined modules is 1.0° in the Helmholtz number range of 2.0–3.0, which is far smaller than the error of 10.1° when using the single modules. Moreover, the truncated stellated octahedral probe, which is composed of a combination of tetrahedral and hexahedral arrays, is the most efficient array configuration for source localization and achieves high precision at high Helmholtz numbers with only five microphones.