Call Today 716.688.4675

Acoustic source localization using circular array microphones

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,\theta, and the range r, are desired. Note that these two parameters, (r,\theta), taken together localize the source precisely.

Figure 1: Circular microphone array topology for 8 microphones, \phi = \frac{2\pi}{7}

 

Define the angle of arrival to be the impinging angle at microphone m_{8} as \theta, using the line joing micrphones m_1 and m_8 as reference. Then the microphones can be easily shown to obey;

dc^2 \left(\tau_{8,9-n}^2-\tau_{8,n}^2 \right) \cos{\left((n-1)\psi\right)} \sin{\theta} + d\left(c^2\tau_{8,9-n}^2 -c^2 \tau_{8,n} -2d^2\right) \sin{\left( (n-1) \psi\right)} \cos{\theta} = c\left(d^2 +c^2 \tau_{8,9-n}\tau_{8,n} \right) \left(\tau_{8,n} - \tau_{8,9-n} \right) , n \in \{2,\cdots,4\}

 

where \tau_{i,j} is the time difference of arrival between the signals at microphones m_{i} and m_{j}.

The least squares solution to solve the angle of arrival, \theta, thus:

\mathbf{A} \begin{bmatrix}\sin{\theta} \\ \cos{\theta} \end{bmatrix} = \mathbf{Y}

 

where

\mathbf{A}=d\begin{bmatrix}c^2 \left(\tau_{8,7}^2-\tau_{8,2}^2 \right) \cos{\left(\psi\right)} & \left(c^2\tau_{8,7}^2 -c^2 \tau_{8,2} -2d^2\right) \sin{\left(\psi\right)}\\c^2 \left(\tau_{8,6}^2-\tau_{8,3}^2 \right) \cos{\left(2\psi\right)} & \left(c^2\tau_{8,6}^2 -c^2 \tau_{8,3} -2d^2\right) \sin{\left( 2\psi\right)}\\c^2 \left(\tau_{8,5}^2-\tau_{8,4}^2 \right) \cos{\left(3\psi\right)} & \left(c^2\tau_{8,5}^2 -c^2 \tau_{8,4} -2d^2\right) \sin{\left(3 \psi\right)} \end{bmatrix}

 

\mathbf{Y}=c\begin{bmatrix} \left(d^2 +c^2 \tau_{8,7}\tau_{8,2} \right) \left(\tau_{8,2} - \tau_{8,7} \right)\\ \left(d^2 +c^2 \tau_{8,6}\tau_{8,3} \right) \left(\tau_{8,3} - \tau_{8,6} \right)\\ \left(d^2 +c^2 \tau_{8,5}\tau_{8,4} \right) \left(\tau_{8,4} - \tau_{8,5} \right) \end{bmatrix}

 

VOCAL Technologies offers custom designed solutions for beamforming with a direction of arrival estimation, 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!

\end{document}

More Information

VOCAL Technologies, Ltd.
520 Lee Entrance, Suite 202
Amherst New York 14228
Phone: +1-716-688-4675
Fax: +1-716-639-0713
Email: sales@vocal.com