Weighted data spaces for correlation-based array imaging in experimental aeroacoustics

Abstract

This article discusses aeroacoustic imaging methods based on correlation measurements in the frequencydomain. Standard methods in this field assume that the estimated correlation matrix is superimposed withadditive white noise. In this paper we present a mathematical model for the measurement process coveringarbitrarily correlated noise. The covariance matrix of correlation data is given in terms of fourth ordermoments. The aim of this paper is to explore the use of such additional information on the measurementdata in imaging methods. For this purpose a class of weighted data spaces is introduced, where each dataspace naturally defines an associated beamforming method with a corresponding point spread function. Thisgeneric class of beamformers contains many well-known methods such as Conventional Beamforming, (Ro-bust) Adaptive Beamforming or beamforming with shading. This article examines in particular weightingsthat depend on the noise (co)variances. In a theoretical analysis we prove that the beamformer, weighted bythe full noise covariance matrix, has minimal variance among all beamformers from the described class. Ap-plication of the (co)variance weighted methods on synthetic and experimental data show that the resolutionof the results is improved and noise effects are reduced.