Comptes Rendus
no. 9-10
Statistics/Theory of Signals
Exact filtering in conditionally Markov switching hidden linear models
[Filtrage exact dans les modèles conditionnellement linéaires à sauts markoviens]

Présenté par : Paul Deheuvels

Wojciech Pieczynski1
1 Institut Telecom, Telecom SudParis, Dept. CITI, CNRS UMR 5157, 91000 Evry, France
Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 587-590.

Dans les modèles classiques linéaires cachés à sauts markoviens, le calcul exact des filtres optimaux est dʼune complexité exponentielle par rapport au nombre dʼobservations, ce qui nécessite lʼutilisation de techniques dʼapproximation. Dans cet article, nous introduisons une nouvelle famille de modèles qui rendent ces opérations possibles en pratique.

In the classical setup of Markov switching hidden linear systems, the exact evaluation of optimal filters requires computations with complexity increasing exponentially with respect to the number of observations. In the present article, we propose a new family of models which overcome this difficulty, and render practically feasible these calculations.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2011.02.007
Wojciech Pieczynski 1

1 Institut Telecom, Telecom SudParis, Dept. CITI, CNRS UMR 5157, 91000 Evry, France 
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Wojciech Pieczynski. Exact filtering in conditionally Markov switching hidden linear models. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 587-590. doi : 10.1016/j.crma.2011.02.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.02.007/

[1] N. Abbassi, W. Pieczynski, Exact filtering in semi-Markov jumping system, in: Sixth International Conference of Computational Methods in Sciences and Engineering, Hersonissos, Crete, Greece, September 25–30, 2008.

[2] C. Andrieu; C.M. Davy; A. Doucet Efficient particle filtering for jump Markov systems. Application to time-varying autoregressions, IEEE Trans. Signal Process., Volume 51 (2003) no. 7, pp. 1762-1770

[3] O. Cappé; E. Moulines; T. Ryden Inference in Hidden Markov Models, Springer, 2005

[4] O.L.V. Costa; M.D. Fragoso; R.P. Marques Discrete Time Markov Jump Linear Systems, Springer-Verlag, New York, 2005

[5] S. Derrode; W. Pieczynski Signal and image segmentation using pairwise Markov chains, IEEE Trans. Signal Process., Volume 52 (2004) no. 9, pp. 2477-2489

[6] P. Giordani; R. Kohn; D. van Dijk A unified approach to nonlinearity, structural change, and outliers, J. Econometrics, Volume 137 (2007), pp. 112-133

[7] W. Pieczynski Multisensor triplet Markov chains and theory of evidence, Internat. J. Approx. Reason., Volume 45 (2007) no. 1, pp. 1-16

[8] W. Pieczynski, Exact calculation of optimal filter in semi-Markov switching model, in: Fourth World Conference of the International Association for Statistical Computing (IASC 2008), Yokohama, Japan, December 5–8, 2008.

[9] J.K. Tugnait Adaptive estimation and identification for discrete systems with Markov jump parameters, IEEE Trans. Automat. Control, Volume AC-25 (1982), pp. 1054-1065

[10] O. Zoeter; T. Heskes Deterministic approximate inference techniques for conditionally Gaussian state space models, Statist. Comput., Volume 16 (2006), pp. 279-292

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