Estimations pour les modèles de Markov cachés et approximations particulaires : Application à la cartographie et à la localisation simultanées.

Abstract : This document is dedicated to inference problems in hidden Markov models. The first part is devoted to an online maximum likelihood estimation procedure which does not store the observations. We propose a new Expectation Maximization based method called the Block Online Expectation Maximization (BOEM) algorithm. This algorithm solves the online estimation problem for general hidden Markov models. In complex situations, it requires the introduction of Sequential Monte Carlo methods to approximate several expectations under the fixed interval smoothing distributions. The convergence of the algorithm is shown under the assumption that the Lp mean error due to the Monte Carlo approximation can be controlled explicitly in the number of observations and in the number of particles. Therefore, a second part of the document establishes such controls for several Sequential Monte Carlo algorithms. This BOEM algorithm is then used to solve the simultaneous localization and mapping problem in different frameworks. Finally, the last part of this thesis is dedicated to nonparametric estimation in hidden Markov models. It is assumed that the Markov chain (Xk) is a random walk lying in a compact set with increment distribution known up to a scaling factor a. At each time step k, Yk is a noisy observations of f(Xk) where f is an unknown function. We establish the identifiability of the statistical model and we propose estimators of f and a based on the pairwise likelihood of the observations.
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Sylvain Le Corff. Estimations pour les modèles de Markov cachés et approximations particulaires : Application à la cartographie et à la localisation simultanées.. Mathématiques générales [math.GM]. Télécom ParisTech, 2012. Français. ⟨NNT : 2012ENST0052⟩. ⟨tel-01077883⟩

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