I have a box with four microphones on its sides: one on top, one on front and two on left and right sides.
Is it possible to calculate a vector from the center of the box to the source of sound in real time?
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Is it possible to calculate vector from center of box to the source of sound realtime?
Theoretically yes. As long as the microphones are no co-planar or co-linear, 4 is fine.
You can use cross correlation to determine the time of arrival difference between any two microphones. Using a proper geometric transform you can calculate the direction of arrival estimate.
The easiest 4-microphone configuration has the shape of coordinate system: one microphone at the origin and one each one unit distance away on the X, Y, and Z directions respectively.
The devil is in the details though. Things to tackle are