Compensation of inherent bias errors in using the three-dimensional acoustic intensimetry for sound source localization

Abstract

The three-dimensional acoustic intensimetry has not been found useful for the sound source localization, although it was developed a long time ago. One of the leading causes is the significant amount of inherent bias error in the measured intensity vector. In addition to the well-known phase mismatch and finite difference errors, the two crucial bias error mechanisms exist yet. Both of them are principally caused by employing the limited number of microphones in estimating the direction-of-arrival vector. One is the spectral bias error exhibiting a significant fluctuation in the intensity spectrum, which is due to the time-delay of the incident and reflected sounds travelling between microphones. The other is the spatial bias error exhibiting the intensity variation depending on the probe orientation, which is due to the spatial inhomogeneity of the microphone distribution. In this work, two parameters are considered in the compensation of spectral bias error: the phase of cross-spectrum and the time contents of cross-correlation function. Also, an error map associated with the incident direction of sound is calculated for a sphere surrounding the probe to compensate for the spatial bias error. Experiments are conducted with two different source types emitting a band-limited noise and an impulsive sound, and also varying the source positions to investigate the effect of main parameters. A tetrahedral intensity probe consisted of 4 pressure microphones with 30-mm spacing is used for the test in a reverberant space. The result shows that the mean localization error is less than 3° for 0.3 < kd < 2.5, while the error without compensation is 18°. It is found that the spectral bias error can be reduced effectively by using the linearized phase of the cross-spectrum or the cross-correlation function with the truncated early-time components only.