Bayesian microphone position estimation for the transfer function tube method of acoustic impedance measurements

The transfer functions of multiple microphones inside the impedance tube are widely used to derive the acoustic properties from experimental data, including normal incidence sound absorption/reflection, and characteristic impedance of porous media. It is well known that the measurement results from the normal incidence tube techniques are highly sensitive to precise microphone phase-matches and accurate microphone positions. Knowledge of the equivalent acoustic center of the microphones is required to obtain an accurate normal incidence measurement inside the tube. This paper discusses accurate and deliberate processes to locate the equivalent acoustic center of the microphones. A model of the reflection coefficient for a hypothetical air layer inside the tube and in front of a rigid back is used with the model-based Bayesian parameter estimation, to infer equivalent microphone positions. One calibration measurement of the transfer function between microphones is conducted to infer the equivalent microphone positions in the impedance tube. The model-based Bayesian method will be able to provide accurate acoustic centers for each necessary microphone without an additional microphone position. This paper discusses in detail the formulation of Bayesian parameter estimation, the model used, and the experimental results on estimated mean microphone positions and their uncertainties.