The Maximally-Coherent Reference technique and its application to sound source extraction without synchronous measurements

Abstract

In source identification, it is often necessary to perform source extraction, and in cases involving sequential measurements, to also perform resynchronization. Coherence techniques, which are based on the use of references (i.e., fixed sensors), are widely used to solve these two equivalent problems. However, when the number of references surpasses the number of sources, the cross-spectral matrix becomes ill-conditioned, invalidating the popular least squares (LS) solution. Although the truncated singular value decomposition (TSVD) was successfully applied in the literature to solve this problem, its validity is limited to the case of scalar noise on the references. It is also difficult to apply, when the singular values are gradually decreasing. This paper proposes a solution based on a set of virtual references that is maximally correlated with the measurements, named the Maximally-Coherent Reference (MCR) technique, accompanied with a technique for estimating the number of sources. The method is validated using both numerical and physical laboratory experiments, and by using real acoustical data from an e-motor. It is shown to return better results than LS and TSVD when employed for the same purpose.