Seminario Dottorato: Identification of Reciprocal Processes and related Matrix Extension Problem

Wednesday 8 June 2011 - Francesca Carli

ARGOMENTI: Seminars Ph.D. Program

Wednesday 8 June 2011 h. 14:30, room 2BC60
Francesca Carli (Padova - D.E.I.)
"Identification of Reciprocal Processes and related Matrix Extension Problem"

Stationary reciprocal processes defined on a finite interval of the integer line can be seen as a special class of Markov random fields restricted to one dimension. This kind of processes are potentially useful for describing signals which naturally live in a finite region of the time (or space) line. Non-stationary reciprocal processes have been extensively studied in the past especially by Jamison, Krener, Levy and co-workers. The specialization of the non-stationary theory to the stationary case, however, does not seem to have been pursued in sufficient depth in the literature. Moreover, estimation and identification of reciprocal stochastic models starting from observed data seems still to be an open problem.
This talk addresses these problems showing that maximum likelihood identification of stationary reciprocal processes on the discrete circle leads to a covariance extension problem for block-circulant covariance matrices. This generalizes the famous covariance band extension problem for stationary processes on the integer line. We show that the maximum entropy principle leads to a complete solution of the problem. An efficient algorithm for the computation of the maximum likelihood estimates is also provided.

Rif. int. C. Marastoni, T. Vargiolu

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