On the existence of a solution to a spectral estimation problem \emph{\`a la} Byrnes-Georgiou-Lindquist

TL;DR

This paper proves that a solution exists for a broad class of spectral estimation problems, extending previous results limited to special cases, using topological degree theory.

Contribution

It generalizes the existence proof for spectral estimation solutions to arbitrary prior densities, employing topological degree theory.

Findings

Solution exists for any matrix-valued prior density

Extends previous special-case results

Uses topological degree theory as main tool

Abstract

A parametric spectral estimation problem in the style of Byrnes, Georgiou, and Lindquist was posed in \cite{FPZ-10}, but the existence of a solution was only proved in a special case. Based on their results, we show that a solution indeed exists given an arbitrary matrix-valued prior density. The main tool in our proof is the topological degree theory.