Effect of the Error on the Sound Speed and Microphone Position on Acoustic Image Obtained with a Spherical Microphone Array

Abstract

In order to reduce the noise level in a workplace, the main sources have to be localized. This task can be done with a spherical microphone array (SMA). When the microphones are flush mounted to a rigid sphere surface, the SMA is referred to as rigid. In this case, the Spherical Harmonic Beamforming (SHB) algorithm is preferred since it allows to account for the scattering effect of the acoustic waves on the rigid sphere. When the microphones are fixed on an open wire frame, i.e., transparent with respect to the acoustic waves, the SMA is referred to as open and the Generalized Cross-Correlation (GCC) algorithm in the time domain can be used. Both algorithms require the knowledge of the sound speed and the microphones position. In this study, the effect on the acoustic image of an error committed on these parameters is investigated numerically. The error is introduced by using a reference value for both parameters which is different from the one used to generate the microphones signals. More specifically, the microphones signals captured by a rigid or an open SMA placed in a room are obtained numerically using a sampled range of sound speed values and degrees of precision of microphone position. Then these signals are used as input to the SHB and GCC algorithms to calculate the acoustic image but with the reference value for the sound speed and the microphone position instead of those used to generate the input signals. The main lobe area is the criterion used to evaluate the parameters influence on the acoustic image. The results show that both algorithms are sensitive to the sound speed uncertainty, while the microphones position uncertainty affects more the SHB than the BF.