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Beamforming by means of the Mahalanobis distance

Raumer, Hans-Georg (2019) Beamforming by means of the Mahalanobis distance. In: Inter-Noise 2019 (1646), pp. 1-8. Inter-Noise 2019, 16.-19. June 2019, Madrid, Spain.

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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.

Item URL in elib:https://elib.dlr.de/127986/
Document Type:Conference or Workshop Item (Speech)
Title:Beamforming by means of the Mahalanobis distance
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Raumer, Hans-Georghans-georg.raumer (at) dlr.dehttps://orcid.org/0000-0001-6727-6819
Date:June 2019
Journal or Publication Title:Inter-Noise 2019
Refereed publication:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Page Range:pp. 1-8
Editors:
EditorsEmail
UNSPECIFIEDSEA, i-ince
Series Name:Conference Proceedings online
Status:Published
Keywords:array imaging, noise model, beamforming, source localization
Event Title:Inter-Noise 2019
Event Location:Madrid, Spain
Event Type:international Conference
Event Dates:16.-19. June 2019
Organizer:Spanish Acoustical Society (SEA)
Institution:Deutsches Zentrum für Luft- und Raumfahrt e.V.
Department:AS-EXV
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation and Validation
Location: Göttingen
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > Experimental Methods, GO
Deposited By: Micknaus, Ilka
Deposited On:17 Jul 2019 11:16
Last Modified:17 Jul 2019 11:41

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