New results on state-space and input-output identification of non-gaussian processes using cumulants

Georgios B. Giannakis, Ananthram Swami

Research output: Contribution to journalArticle

15 Scopus citations

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 allpass 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.

Original languageEnglish (US)
Pages (from-to)199-204
Number of pages6
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume826
DOIs
StatePublished - Jan 21 1988

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