21 January 1988 New Results On State-Space And Input-Output Identification Of Non-Gaussian Processes Using Cumulants
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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, 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); doi: 10.1117/12.942033; https://doi.org/10.1117/12.942033
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