Procedure for the Accurate Phase Calibration of a Microphone Array

Abstract

The "delay and sum beamformer" algorithm (\DSB") is a powerful tool for the localisation and quantioncation of acoustic sources with microphone arrays. For the calculation of beamforming maps the DSB algorithm requires the following input data: time series of all microphones, a grid of focus points which includes the region of interest, paramater of the ow for boundary layer or shear layer corrections and the accurate position of all microphones. The present paper is focused on the last item: the accurate estimation of the microphone positions. Especially for aeroacoustic applications the number of microphones should be large enough in order to obtain good beamforming results. The estimation of the accurate microphone positions can mean a huge time consuming effort. The method which will be presented in this paper is similar to the well known global positioning system: distances to satellites provide information about the position of a receiver. Here, several monopole-like acoustical point sources with known positions and a reference microphone which is installed close to the sound sources are used to compute the position of the microphones of a microphone array in the three-dimensional space. After pointing out the basic concepts and algorithms a practical implementation of the test sources is described. Eight test sources and the reference microphone are integrated in a so-called calibration unit. Afterwards a calibration of a microphone array with known microphone positions is presented to verify the method and to assess the accuracy that can be achieved. Furthermore the problem is addressed how many test sources are necessary to achieve accurate results. Finally, the procedure is used to calibrate an out-of-flow microphone array with a layout of microphones where the positions are only known with some uncertainty. Investigations concerning the frequency dependence of the calibration are presented. Beamforming on a loudspeaker is performed to show in how far more accurately known microphone positions can improve beamforming results, particularly in the higher frequency range.