Weighted Data Spaces for Correlation-Based Array Imaging in Experimental Aeroacoustics

TL;DR

This paper introduces a mathematical framework for correlation-based aeroacoustic imaging that accounts for correlated noise, proposing weighted data spaces and beamformers that improve resolution and noise reduction in experimental data.

Contribution

It develops a novel class of weighted data spaces and beamformers incorporating correlated noise information, enhancing imaging accuracy in aeroacoustics.

Findings

Weighted beamformers reduce noise effects.

Full noise covariance weighting improves resolution.

Method outperforms standard techniques on synthetic and experimental data.

Abstract

This article discusses aeroacoustic imaging methods based on correlation measurements in the frequency domain. Standard methods in this field assume that the estimated correlation matrix is superimposed with additive white noise. In this paper we present a mathematical model for the measurement process covering arbitrarily correlated noise. The covariance matrix of correlation data is given in terms of fourth order moments. The aim of this paper is to explore the use of such additional information on the measurement data in imaging methods. For this purpose a class of weighted data spaces is introduced, where each data space naturally defines an associated beamforming method with a corresponding point spread function. This generic class of beamformers contains many well-known methods such as Conventional Beamforming, (Robust) Adaptive Beamforming or beamforming with shading. This article examines in particular weightings that depend on the noise (co)variances. In a theoretical analysis we prove that the beamformer, weighted by the full noise covariance matrix, has minimal variance among all beamformers from the described class. Application of the (co)variance weighted methods on synthetic and experimental data show that the resolution of the results is improved and noise effects are reduced.