A new family of high-resolution multivariate spectral estimators

TL;DR

This paper introduces a new family of high-resolution multivariate spectral estimators based on extending the Beta divergence, connecting existing divergence measures, and providing a spectrum approximation framework with practical simulation insights.

Contribution

It extends the Beta divergence to multivariate spectral densities, linking it to existing measures and developing a new spectral estimation method with characterized solution families.

Findings

The Beta divergence family smoothly connects multivariate Kullback-Leibler and Itakura-Saito distances.

A spectrum approximation problem is formulated and solved within this new divergence framework.

Simulations indicate the optimal solution depends on specific estimation features.

Abstract

In this paper, we extend the Beta divergence family to multivariate power spectral densities. Similarly to the scalar case, we show that it smoothly connects the multivariate Kullback-Leibler divergence with the multivariate Itakura-Saito distance. We successively study a spectrum approximation problem, based on the Beta divergence family, which is related to a multivariate extension of the THREE spectral estimation technique. It is then possible to characterize a family of solutions to the problem. An upper bound on the complexity of these solutions will also be provided. Simulations suggest that the most suitable solution of this family depends on the specific features required from the estimation problem.