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Chaînes de Markov triplets et filtrage optimal dans les systemes à sauts

Abstract : This thesis is devoted to the restoration problem and the parameter estimation by filtering in the traditional hidden Markov chain model, couple and triplet with Markovian jumps. We propose two new approximate methods in the case of Gaussian linear systems with Markovian jumps. first is founded to use the hidden Markov chains by noise with long memory, we obtains a method " partially not supervised" some parameters, can be estimated by using an adaptive version of EM or ICE algorithm, the results obtained are encouraging and comparable with the methods used classically (Kalman/Particle). The second one exploits idea to keep at every moment only the most probable trajectories; we obtains a very fast method giving very interesting results. Then we propose two families of models to jumps which are original. The first one is very general where the process couples made up of the hidden and the observations process conditionally to the jumps, are a hidden Markov chain, and we propose an extension of particulate filtering to this family. The second is under family of the first, where the couple made up of the jumps and the observations process is Markovian, in this last case exact optimal filtering is possible with a linear complexity in time. Using of the second family to approach the first one is studied and the results exposed in this memory seem very encouraging
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Submitted on : Wednesday, October 16, 2013 - 10:32:11 AM
Last modification on : Wednesday, October 14, 2020 - 4:09:17 AM
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  • HAL Id : tel-00873630, version 1

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Noufel Abbassi. Chaînes de Markov triplets et filtrage optimal dans les systemes à sauts. Architecture, aménagement de l'espace. Institut National des Télécommunications, 2012. Français. ⟨NNT : 2012TELE0018⟩. ⟨tel-00873630⟩

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