Space-time covariance matrix factorisation and estimation for broadband multichannel problems, part 2 : eigenvalue decomposition

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Proudler, Ian K. and Weiss, Stephan (2025) Space-time covariance matrix factorisation and estimation for broadband multichannel problems, part 2 : eigenvalue decomposition. In: 23rd IEEE Statistical Signal Processing Workshop, 2025-06-08 - 2025-06-11.

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Abstract

As part of the SSP tutorial on space-time covariance matrix factorisation and estimation for broadband multichannel problems, this part II specifically addresses factorisations: this includes the theoretical existence of an analytic eigenvalue decomposition, and relates this to a number of algorithmic solutions. The overall tutorial addresses recent developments in formulating and solving broadband multichannel problems through matrices of functions and their factorisations, such as the analytic eigenvalue decomposition of the space-time covariance, or an analytic singular value decomposition applied to a data model. This can generalise well known formulations of narrowband problems using covariance matrices, and of narrowband solutions via their diagonalisation, to the broadband case. We present theoretical background on the factorisation of matrices of functions, and show how the estimation of the statistical parameters impacts on the perturbation of the ground truth factors of a decomposition. We review a number of algorithms, and discuss some sample applications such as direction of arrival estimation, beamforming, weak transient signal and subspace detection, MIMO communications, speech enhancement, or source separation.

ORCID iDs

Proudler, Ian K. and Weiss, Stephan ORCID logoORCID: https://orcid.org/0000-0002-3486-7206;
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