Innovation Models in a Stochastic System Represented by an Input-Output Model

Kuniharu KISHIDA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.8   pp.1337-1344
Publication Date: 1994/08/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
innovation model,  matrix Riccati equation,  zeros,  generalized eigenvalue problem,  stochastic process,  

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A stochastic system represented by an input-output model can be described by mainly two different types of state space representation. Corresponding to state space representations innovation models are examined. The relationship between both representations is made clear systematically. An easy transformation between them is presented. Zeros of innovation models are the same as those of an ARMA model which is stochastically equivalent to innovation models, and related to stable eigenvalues of generalized eigenvalue problem of matrix Riccati equation.