1 - Le filtrage de Wiener linéaire-quadratique à horizon fini: application à la prédiction

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URI: http://hdl.handle.net/2042/1695
Title: 1 - Le filtrage de Wiener linéaire-quadratique à horizon fini: application à la prédiction
Author: DUVAUT (P.)
Abstract: Une approche du filtrage de Wiener, dans le cas d'un processus réel de moments finis est proposée puis appliquée à la prédiction de même nature. Le rôle crucial des moments de troisième ordre est mis en avant tant dans la représentation du filtrage que dans celle du filtre optimal ou dans l'évaluation de la variance d'estimation
Description: An approach to linear-quadratic Wiener filtering, in the case of a real valued discrete time stochastic process, with finite moments up to the fourth order is given and then extended to the prediction problem . The crucial yole played by the third order moments is pointed out through ail the derivations ranging fi •o m the representation of lq filtering, or the calculation of the optimal frlter to the foret of the variance of the estimate . It is shown that the performance of a linear filter is always improved by the use of a quadratic term, whenever the observation and the unknown processes are not,jointly gaussian . The amount by which the variance decreases is explicitely determined, whatever the statistical properties of the underlying process are . In order to display the opportunity of a quadratic filtering, a particular fantily of stochastic processes is introduced . A case of null linear estimation and, simultaneously, singular quadratic estimation is raised up . Finally, it is argued that when the third order moments are vanishing, the quadratic part of a predictor vasnishes also .
Subject: Filtrage; Filtrage Wiener; Méthode moment; Prédiction; Estimation; Performance; Filtrage linéaire quadratique
Publisher: GRETSI, Saint Martin d'Hères, France
Date: 1989

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