New Results On State-Space And Input-Output Identification Of Non-Gaussian Processes Using Cumulants

Georgios B. Giannakis; Ananthrarn Swami

doi:10.1117/12.942033

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21 January 1988 New Results On State-Space And Input-Output Identification Of Non-Gaussian Processes Using Cumulants

Georgios B. Giannakis, Ananthrarn Swami

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Proceedings Volume 0826, Advanced Algorithms and Architectures for Signal Processing II; (1988) https://doi.org/10.1117/12.942033
Event: 31st Annual Technical Symposium on Optical and Optoelectronic Applied Sciences and Engineering, 1987, San Diego, CA, United States

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.

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Georgios B. Giannakis and Ananthrarn Swami "New Results On State-Space And Input-Output Identification Of Non-Gaussian Processes Using Cumulants", Proc. SPIE 0826, Advanced Algorithms and Architectures for Signal Processing II, (21 January 1988); https://doi.org/10.1117/12.942033

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