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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 177-182 (février 2008)
Doi : 10.1016/j.crma.2007.12.006
Received : 17 October 2006 ;  accepted : 11 December 2007
Extension du filtre de Chandrasekhar au cas des modèles espace d’état périodiques
Extension of the Chandrasekhar filter to the case of periodic state-space models

Abdelhakim Aknouche , Fayçal Hamdi
U.S.T.H.B., Faculté de mathématiques, El Alia, BP 32, Bab Ezzouar, 16111 Algers, Algeria 


Cette Note généralise les équations récurrentes de type Chandrasekhar due à Morf, Sidhu et Kailath (1974) au cas de modèles espace d’états à coefficients périodiques. Nous montrons que la différence d’ordre S de la matrice de covariance de l’erreur de prédiction vérifie certaines équations récurrentes à partir desquelles nous obtenons quelques algorithmes pour l’estimation linéaire des moindres carrés des modèles espace d’état périodiques. Les équations proposées ont des avantages potentiels par rapport au filtre de Kalman et en particulier à l’équation aux différences de Riccati périodique. Pour citer cet article : A. Aknouche, F. Hamdi, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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This Note extends the Chandrasekhar-type recursions due to Morf, Sidhu, and Kailath (1974) to the case of periodic time-varying state-space models. We show that the S -lagged increments of the one-step prediction error covariance satisfy certain recursions from which we derive some algorithms for linear least squares estimation for periodic state-space models. The proposed recursions have potential computational advantages over the Kalman Filter and, in particular, the periodic Riccati difference equation. To cite this article: A. Aknouche, F. Hamdi, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.

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