Planar spherical diffraction-arrays: Linear sound localization algorithms

Sound source localization systems typically measure differences in time-of-arrival between microphones in free field arrays. Using a different concept, we previously designed and built a localization system that mimics nature's solution of harnessing wave diffraction about the head while relying only on two sensors positioned antipodally. Departing from the biological constraint of two sensors, I recently showed that for broadband sources, a high acuity array could be designed with merely three microphones. Yet adding more microphones may further increase acuity and robustness. The localization algorithm we have developed uses pair-wise comparisons between microphones, the number of which increases quadratically with the number of microphones, N. In order to minimize calculations in time sensitive applications, choosing a subset of pairs may be important. I examine this issue here through simulations of a hexagonal array. Thanks to the redundancy of spatial information contained in multiple microphone measurements, algorithms that are linear in N allow high acuity localization of broadband sources.