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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2015

Optimal Filter Approximations in Conditionally Gaussian Pairwise Markov Switching Models

Résumé

—We consider a general triplet Markov Gaussian linear system (X, R, Y), where X is an hidden continuous random sequence, R is an hidden discrete Markov chain, Y is an observed continuous random sequence. When the triplet (X, R, Y) is a classical " Conditionally Gaussian Linear State-Space Model " (CGLSSM), the mean square error optimal filter is not workable with a reasonable complexity and different approximate methods, e.g. based on particle filters, are used. We propose two contributions. The first one is to extend the CGLSSM to a new, more general model, called the " Conditionally Gaussian Pairwise Markov Switching Model " (CGPMSM), in which X is not necessarily Markov given R. The second contribution is to consider a particular case of CGPMSM in which (R, Y) is Markov and in which an exact filter, optimal in the sense of mean square error, can be performed with linear-time complexity. Some experiments show that the proposed method and the suited particle filter have comparable efficiency, while the second one is much faster. Index Terms—Conditionally Gaussian linear state-space model, conditionally Gaussian pairwise markov switching model, exact optimal filtering, Gaussian switching system, hidden Markov models.
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Dates et versions

hal-01157814 , version 1 (28-05-2015)

Identifiants

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N Abbassi, Dalila Benboudjema, Stéphane Derrode, W Pieczynski. Optimal Filter Approximations in Conditionally Gaussian Pairwise Markov Switching Models. IEEE Transactions on Automatic Control, 2015, 60 (4), pp.1104-1109. ⟨10.1109/TAC.2014.2340591⟩. ⟨hal-01157814⟩
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