Bayesian Parameter estimation of microphone positions, sound speed and dissipation for impedance tube measurements

Abstract

With tube measurement widely used for acoustic measurements, calibration plays an important role in verifying and validating the measurement. This work applies a Bayesian method based on an air layer reflectance model to estimate the microphone positions, and sound speed in consideration of environmental effects on uncertainties of the normal incident impedance tube measurements. Bayesian theorem is applied to estimate the microphone positions and sound speed given the experimental data obtained from the transfer function method (TFM) in tube measurements. With a hypothetical air layer treated as material under test in front of a rigid backing in the tube, a parametric model is established for the TFM tube measurement to estimate the microphone positions using Bayesian inference. With the microphone positions accurately estimated, sound speed and losses due to tube interior boundary effects are also estimated within the same Bayesian framework. Bayesian analysis results show that Bayesian parameter estimation based on the air layer model is well suited in estimating the sound speed, microphone positions, and other parameters to ensure highly accurate tube measurements.