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ARMA order estimation via matrix perturbation theory

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1 Author(s)
Fuchs, J.J. ; IRISA Unierviste de Rennes I, Campus de Beaulieu, Rennes Cédex, France and CRECO CNRS Systemes Adaptatifs, France

Using matrix perturbation theory, we obtain the statistical distribution of the smallest eigenvalue of the Hankel matrix built upon the estimated covariances, under the hypothesis that the corresponding exact Hankel matrix possesses one single zero eigenvalue. This allows us to develop and justify a new order determination scheme, whose performance appears similar to those based on likelihood maximization, but with a much lower computational complexity.

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Automatic Control, IEEE Transactions on  (Volume:32 ,  Issue: 4 )