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Proceedings Paper

New Results On State-Space And Input-Output Identification Of Non-Gaussian Processes Using Cumulants
Author(s): Georgios B. Giannakis; Ananthrarn Swami
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Paper Abstract

Closed form expressions and recursive equations relating the parameters of an ARMA model (which may be non-minimum phase, non-causal or may even contain all-pass factors) with the cumulants of its output, in response to excitation by a non-Gaussian i.i.d. process are derived. Based on these relationships, system identification and order determination algorithms are developed. The output noise may be colored Gaussian or i.i.d. non-Gaussian. When a state-space representation is adopted, the stochastic realization problem reduces to the balanced realization of an appropriate Hankel matrix formed by cumulant statistics. Using a Kronecker product formulation, an exact expression is presented for identifying state-space quantities when output cumulants are provided, or for computing output cumulants when the state-space triple is known. If a transfer function approach is employed, cumulant based recursions are proposed to reduce the AR parameter estimation problem to the solution of a system of linear equations. Closed form expressions and alternative formulations are given to cover the case of non-causal processes.

Paper Details

Date Published: 21 January 1988
PDF: 6 pages
Proc. SPIE 0826, Advanced Algorithms and Architectures for Signal Processing II, (21 January 1988); doi: 10.1117/12.942033
Show Author Affiliations
Georgios B. Giannakis, University of Virginia (United States)
Ananthrarn Swami, University of Southern California (United States)

Published in SPIE Proceedings Vol. 0826:
Advanced Algorithms and Architectures for Signal Processing II
Franklin T. Luk, Editor(s)

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