Compensation of spatial bias error in the acoustic intensimetry-based source localization by using an octahedron microphone array

Sound intensimetry can be used for the localization of the sound source by utilizing a compact-sized probe system. While vector sensors are advantageous due to their small size and elimination of finite difference errors, their high initial cost and lack of measurement traceability present implementation challenges. As a result, microphone arrays remain widely used for estimating sound intensity vectors despite their limitations, including a limited frequency range due to the spatial bias error at high Helmholtz numbers. In this study, the spatial bias error is explained theoretically, and the localization errors for different Helmholtz numbers are analyzed using the proposed error model. In addition, the collimation error and its effect on the localization result are analyzed, which was not explained in the error compensation model in previous studies. As an effective configuration, this study proposes an octahedron microphone array consisting of six microphones for sound source localization using acoustic intensimetry. The closed-form solution to calculate one-dimensional intensity vector coefficients based on the microphone position is applied to implement acoustic intensimetry. The microphone array combination method is applied to compensate for spatial bias error, with its validity explained by analyzing the directional response and experimental test results. A double tetrahedron array module and phase and amplitude gradient estimating methods, proposed in previous studies to compensate for spatial bias error, are compared with the suggested method through numerical simulations. The causes of errors at the narrow frequencies found in experimental results and the space efficiency in the practical implementation of the microphone array are discussed. Finally, it is shown that by applying an octahedron microphone array consisting of six microphones and an array combination method, the direction of arrival of the sound source can be accurately estimated, even at high Helmholtz numbers.