A Unifying Maximum-Likelihood View of Cumulant and Polyspectral Measures for Non-Gaussian Signal Classification and Estimation

Georgios B. Giannakis, Michail K. Tsatsanis

Research output: Contribution to journalArticlepeer-review

77 Scopus citations

Abstract

Classification and estimation of non-Gaussian signals observed in additive Gaussian noise of unknown covariance is addressed using cumulants or polyspectra. By integrating ideas from pattern recognition and model identification, asymptotically optimum maximum-likelihood classifiers and ARMA parameter estimators are derived without knowledge of the data distribution. Identifiability of noncausal and nonminimum phase ARMA models is established using a finite number of cumulant or polyspectral lags of any order greater than two. A unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms. Tentative order determination and model validation tests for non-Gaussian ARMA processes are described briefly. Illustrative simulations are also presented.

Original languageEnglish (US)
Pages (from-to)386-406
Number of pages21
JournalIEEE Transactions on Information Theory
Volume38
Issue number2
DOIs
StatePublished - Mar 1992

Bibliographical note

Funding Information:
Manuscript received March 22, 1990; revised July 25, 1991. This work was supported by HDL Contract 5-25227 and U.S. Army LabCom Contract 5-25254. This work was presented at the Conference on Information Sciences and Systems (CISS’90), Princeton, NJ, March 1990. The authors are with the Department of Electrical Engineering, University of Virginia, Charlonesville, VA 22903-2442. IEEE Log Number 9104806.

Keywords

  • ARMA models
  • Classification
  • cumulants
  • estimation
  • identifiability
  • non-Gaussian processes
  • pattern recognition
  • polyspectra

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