We show an approach to localizing an acoustic source using a circular microphone topology. Consider the circular array illustrated in Figure 1 below and suppose the angle of arriving signal,, and the range , are desired. Note that these two parameters, , taken together localize the source precisely.
Figure 1: Circular microphone array topology for microphones,
Define the angle of arrival to be the impinging angle at microphone as , using the line joing micrphones and as reference. Then the microphones can be easily shown to obey;
where is the time difference of arrival between the signals at microphones and .
The least squares solution to solve the angle of arrival, , thus:
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