Beamforming by means of the Mahalanobis distance

Abstract

Conventional beamforming is one of the standard methods for array imaging of acoustic sources. It offers a very robust indicator for the sound source distribution. In conventional beamforming the deviation of model and measurement with respect to the standard 2-norm is minimized. This can be interpreted as the Mahalanobis distance of measurement and model, where the covariance matrix of the measurement noise vector is a positive multiple of the Identity matrix. In real life applications this ideal noise model is often violated and hence the components of the noise vector have different variances or are even correlated. In order evaluate the Mahalanobis distance of model and measurement we need to know the covariance matrix of the noise vector. The covariance matrix can be estimated by the measurement samples or alternatively by an explicit formula assuming the noise is Gaussian. If the covariance matrix is assumed to be diagonal, the Mahalanobis distance can be interpreted as a weighted standard 2-norm, where the weights indicate the reliability of each data point. The application of this approach on experimental data of a wind tunnel test show that the resolution of the source maps can be enhanced compared to conventional beamforming. Conventional beamforming is one of the standard methods for array imaging of acoustic sources. It offers a very robust indicator for the sound source distribution. In conventional beamforming the deviation of model and measurement with respect to the standard 2-norm is minimized. This can be interpreted as the Mahalanobis distance of measurement and model, where the covariance matrix of the measurement noise vector is a positive multiple of the Identity matrix. In real life applications this ideal noise model is often violated and hence the components of the noise vector have different variances or are even correlated. In order evaluate the Mahalanobis distance of model and measurement we need to know the covariance matrix of the noise vector. The covariance matrix can be estimated by the measurement samples or alternatively by an explicit formula assuming the noise is Gaussian. If the covariance matrix is assumed to be diagonal, the Mahalanobis distance can be interpreted as a weighted standard 2-norm, where the weights indicate the reliability of each data point. The application of this approach on experimental data of a wind tunnel test show that the resolution of the source maps can be enhanced compared to conventional beamforming.