Abstract
Classification and estimation of non-Gaussian signals observed in additive Gaussian noise of unknown covariance are addressed using cumulants or polyspectra. By integrating ideas from pattern recognition and model identification, asymptotically optimum maximum-likelihood classifiers and ARMA (autoregressive moving average) 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Keywords
IdentifiabilityEstimatorAutoregressive modelAutoregressive–moving-average modelMathematicsGaussianEstimation theoryCovarianceGaussian noisePattern recognition (psychology)AlgorithmLinear discriminant analysisNoise (video)Artificial intelligenceStatisticsComputer science
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Publication Info
- Year
- 1992
- Type
- article
- Volume
- 38
- Issue
- 2
- Pages
- 386-406
- Citations
- 96
- Access
- Closed
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Cite This
Georgios B. Giannakis,
M.K. Tsatsanis
(1992).
A unifying maximum-likelihood view of cumulant and polyspectral measures for non-Gaussian signal classification and estimation.
IEEE Transactions on Information Theory
, 38
(2)
, 386-406.
https://doi.org/10.1109/18.119695
Identifiers
- DOI
- 10.1109/18.119695