Acoustic Vector Sensing

Undergraduate Research by Ian Beil and Evan Nixon

Capon Spectrum Beamforming

Beamforming is a spatial filtering technique used in signal processing. It is frequently utilized in sensor arrays  to determine the angle of arrival of a signal when noise is present. Capon Spectrum Beamforming is a minimum-variance, distortionless response technique. This means that it optimizes the signal to noise ratio of the beam, without affecting the gain or phase of the signal.

 

Our application of Beamforming can be broken down into a fairly simple idea: we essentially created a series of filters which maximized the gain of our signal at various azimuth and elevation angles. Using these filters we could iterate over the surface of a sphere to determine the different energy levels from different directions. Then it is a simple matter of finding the maximum energy to locate the direction of arrival of a sound source.

 

We used a data dependent beamformer built based on the following measurement models:

 

Single AVS Model

 

Each AVS measures sound and particle velocity, but also receives noise. In this situation we used the following equation to model the sound from the AVS:

Where

Multiple AVS Model

 

For multiple sensors we used the following model:

Where

Estimation Algorithm

The angle of arrival of the sound wave is estimated by finding the angles that maximize the Capon Spectra [1] :

Where                                                      

with N = the number of samples. R is the

sample correlation matrix.

 

[1] M. Hawkes and A. Nehorai, "Acoustic vector-sensor beamforming and capon direction estimation," IEEE Trans. on Signal Processing, Vol. SP-46, pp. 2291-2304, Sept. 1998.

[2] Van Veen, B.D.; Buckley, K.M. ASSP Magazine, IEEE [see also IEEE Signal Processing Magazine] , Volume: 5 Issue: 2 , April 1988