Signal space geometry
type: Item
instance of: scholarly article
title: Signal space geometry
zbMATH Open document ID: 0621.94004
DOI: 10.1016/0020-0255(86)90014-9
author: R. S. Bucy
published in: Information Sciences
publication date: 1986-01-01T00:00:00Z
review text: In the paper a new approach to the problem of estimating a sum of imaginary exponentials (multiple frequencies) in the presence of noise, assumed to be zero mean Gaussian noise, is presented. The process is available by a set of measurements at the times \(t_ 1,...,t_ n\) and this is performed N times, all the measurements are assumed to be independent. It is shown that the geometric least square criterion can be viewed as that of calculating the shortest distance from a point to a set in a Grassmannian manifold with a coordinate free metric. We think that this approach can reveal new applications of differential geometry in estimation theory.
Mathematics Subject Classification ID: 94A14
zbMATH DE Number: 4008266
zbMATH Keywords: exterior algebra of Grassmann
zbMATH Keywords: signal restoration in the presence of noise
zbMATH Keywords: multiple frequencies
zbMATH Keywords: differential geometry
zbMATH Keywords: estimation theory
MaRDI profile type: Publication
full work available at URL: 0020-0255(86)90014-9
OpenAlex ID: W2008746375
cites work: Q4130123
cites work: Q5612017
cites work: RELATIONS BETWEEN TWO SETS OF VARIATES
cites work: Q3254327
cites work: Q3897665
cites work: TANGENT BUNDLES, MONOIDAL THEORIES AND WEIL ALGEBRAS
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description: scientific article; zbMATH DE number 4008266