Time domain source localization technique based on generalized cross correlation and generalized mean
Microphone arrays have become efficient tools to localize sound acoustic sources. The standard method is the delay and sum beamforming which can be used in the frequency or time domain. In the frequency domain, the cross spectral matrix of the microphone signals is used to generate the noise source map. Therefore, the processing has to be done frequency by frequency. To improve noise source maps, deconvolution or inverse methods can be utilized. However, these methods increase the computation time and may require user-defined parameters. In the time domain, the generalized cross-correlation of the microphone signals is used to compute the noise source map. The generalized cross-correlation of a microphone pair signal provides the spatial likelihood functions. Then, these spatial likelihood functions are averaged to generate the noise source map. This map is composed of a main lobe which leads to the source position together with side and spurious lobes which may prevent the localization of the source. The spatial likelihood functions averaging process is commonly based on the arithmetic mean. In this study, averaging based on the generalized mean is considered to improve the source localization. Several source-microphone array configurations are numerically computed. Noise source maps obtained with geometric and harmonic means are compared with that based on the classical arithmetic mean. The geometric and harmonic means are shown to provide the best noise source maps with few side lobes. The effect of the number of microphones on the noise source map quality is also investigated.
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