pr\u00e9sentent<\/p>\n\n\n\n
Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Institut Polytechnique de Paris, pr\u00e9par\u00e9 \u00e0 T\u00e9l\u00e9com SudParis en :<\/p>\n\n\n\n
le MERCREDI 26 NOVEMBRE 2025 \u00e0 12h15<\/p>\n\n\n\n
\u00e0<\/p>\n\n\n\n
J004
9 Rue Charles Fourier, \u00c9vry-Courcouronnes, 91011, T\u00e9l\u00e9com SudParis<\/p>\n\n\n\n
Membres du jury :<\/strong><\/p>\n\n\n\n M. Wojciech PIECZYNSKI<\/strong>, Professeur \u00e9m\u00e9rite, T\u00e9l\u00e9com SudParis – Laboratoire SAMOVAR, FRANCE – Directeur de these R\u00e9sum\u00e9 :<\/strong><\/p>\n\n\n\n Les Cha\u00eenes de Markov Cach\u00e9es (HMC) sont fr\u00e9quemment utilis\u00e9es pour le filtrage et la pr\u00e9diction dans l’\u00e9tude des s\u00e9ries temporelles. En particulier, dans le cas gaussien et homog\u00e8ne, le Filtre de Kalman est tr\u00e8s connu pour ses applications en poursuite, m\u00e9t\u00e9orologie, finance… Les HMC sont un cas particulier des Cha\u00eenes de Markov Couple ou Pairwise Markov Chains (PMC), mod\u00e8les qui n’exigent pas, en particulier, la markovianit\u00e9 du processus cach\u00e9. Les apports des PMC par rapport aux HMC pour le filtrage, dans le contexte gaussien homog\u00e8ne, ont d\u00e9j\u00e0 \u00e9t\u00e9 mis en lumi\u00e8re dans un certain nombre de travaux ; leur \u00e9tude dans le cadre de la pr\u00e9diction est originale. S’int\u00e9ressant plus sp\u00e9cifiquement \u00e0 la robustesse, on propose des m\u00e9thodes d’\u00e9valuation analytique de l’accroissement de l’erreur du filtrage ou de la pr\u00e9diction lorsque les param\u00e8tres du PMC utilis\u00e9 s’\u00e9cartent des vrais param\u00e8tres. Une m\u00e9thode s\u00e9quentielle permettant le calcul rapide de leur \u00e9volution dans le temps est propos\u00e9e. En particulier, elle permet l’\u00e9valuation de l’\u00e9volution, au cours du temps, des erreurs du filtre et du pr\u00e9dicteur lorsque les donn\u00e9es correspondant \u00e0 un PMC sont trait\u00e9es en utilisant un HMC. Afin d’illustrer l’apport des PMC par rapport aux HMC dans la pr\u00e9diction de s\u00e9ries temporelles, on compare leurs performances dans le cadre du filtrage et de la pr\u00e9diction de diff\u00e9rentes donn\u00e9es r\u00e9elles (pression, temp\u00e9rature, humidit\u00e9 des sols). Hidden Markov Chains (HMC) are frequently used for filtering and prediction in the study of time series. In particular, in the Gaussian and homogeneous case, the Kalman Filter is well known for its applications in tracking, meteorology, finance… HMCs are a special case of Pairwise Markov Chains (PMCs), models which do not require, in particular, the markovianity of the hidden process. The benefits of PMCs over HMCs for filtering, in the homogeneous Gaussian context, have already been highlighted in a number of works; their study in the context of prediction is original. Focusing more specifically on robustness, we propose methods for analytically evaluating the increase in filtering or prediction error when the PMC parameters used deviate from the true parameters. A sequential method enabling rapid calculation of their evolution over time is proposed. In particular, it enables us to evaluate the evolution, over time, of filter and predictor errors when data corresponding to a PMC are processed using an HMC. To illustrate the contribution of PMCs compared with HMCs in predicting time series, we compare their performance in filtering and predicting different real data (pressure, temperature, soil moisture).<\/p>\n","protected":false},"excerpt":{"rendered":" L’Ecole doctorale : Math\u00e9matiques Hadamard et le Laboratoire de recherche SAMOVAR – Services r\u00e9partis, Architectures, Mod\u00e9lisation, Validation, Administration des R\u00e9seaux pr\u00e9sentent l\u2019AVIS DE SOUTENANCE de Monsieur Marc ESCUDIER Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Institut Polytechnique de Paris, pr\u00e9par\u00e9 \u00e0 T\u00e9l\u00e9com SudParis en : \u00ab \u00c9tude de l\u2019erreur du 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M. Fran\u00e7ois SEPTIER<\/strong>, Professeur des universit\u00e9s, Universit\u00e9 Bretagne Sud – Laboratoire de Math\u00e9matiques de Bretagne Atlantique (LMBA) UMR CNRS 6205, FRANCE – Rapporteur
M. C\u00e9dric RICHARD<\/strong>, Professeur des universit\u00e9s, Universit\u00e9 C\u00f4te d’Azur (Nice Sophia-Antipolis) – Laboratoire Lagrange, Observatoire de la C\u00f4te d’Azur UMR CNRS 7293, FRANCE – Rapporteur
M. Pascal BIANCHI<\/strong>, Professeur des universit\u00e9s, T\u00e9l\u00e9com Paris – Laboratoire Traitement et Communication de l’Information (LTCI) UMR CNRS 5141, FRANCE – Examinateur
M. Pascal LARZABAL<\/strong>, Professeur des universit\u00e9s, Universit\u00e9 Paris-Saclay – Laboratoire SATIE (Syst\u00e8mes et Applications des Technologies de l’Information et de l’\u00c9nergie) UMR CNRS 8029, FRANCE – Examinateur<\/p>\n\n\n\n\u00ab \u00c9tude de l\u2019erreur du Filtre et du Pr\u00e9dicteur dans les mod\u00e8les de Markov Couple Gaussiens \u00bb<\/h2>\n\n\n\n
pr\u00e9sent\u00e9 par Monsieur Marc ESCUDIER<\/h2>\n\n\n\n
Abstract :<\/strong><\/p>\n\n\n\n