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Near field direction of sound source estimate using circular array microphones

There are certain applications where the assumtion that the source of the impinging sound source is far field does not hold. The analytical expressions for far field source localization will thus be laden with large margins of errors. There are certain applications where the assumtion that the source of the impinging sound source is far field does not hold. The analytical expressions for far field source localization will thus be laden with large margins of errors. In such situations, a different solution is required. Suppose there is a near field signal impinging on the circular array microphones as shown in as shown in Figure 1 below:

 

8 microphones

Circular microphone array topology for 8 microphones

Also, suppose the direction of arrival, DOA, of the impinging signal is desired. It is clear that the solutions that assumes that the signal impinges on all microphones at the same angle does not hold. There are 7! time delay of arrivals that can be estimated using pairwise correlates. However, for real time operating systems, RTOSs, we can not utilize all 7! possible delay estimates between paired microphones without depleting considerably computing resources.  A reduction by a factor of 6! is possible by using only 7 time delay of arrivals. It can be shown that by pivoting on a single microphone, the DOA should obey:

dc^2 \left( \tau_{9-n}^2 - \tau_{n}^2\right) \cos{\left((n-1)\psi\right)} \sin{\theta} + d\left(c^2\tau_{9-n}^2 -c^2 \tau_{n} -2d^2\right) \sin{\left( (n-1) \psi\right)}\cos{\theta} = c\left(d^2 +c^2 \tau_{9-n}\tau_{n} \right) \left(\tau_{n} - \tau_{9-n} \right) n \in \{2,\cdots,4\}

Equation (1) can be compressed in matrix form to:

near field angle of arrival equation

A least squares approach can then be used to efficiently compute the DOAs to a resolution of below 7^{\circ} using 8 microphones.

VOCAL Technologies offers custom designed AoA estimation solutions for beamforming with a robust voice activity detector, acoustic echo cancellation and noise suppression. Our custom implementations of such systems are meant to deliver optimum performance for your specific beamforming task. Contact us today to discuss your solution!

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