Étude Statistique du Problème de la Trajectographie Passive

Abstract : This thesis presents a statistical study of the bearings-only tracking problem. In a first part, we deal with the question of observability for parametric and piecewise parametric trajectories and for constant speed trajectories. The second part is dedicated to the estimation: we give the properties of the maximum likelihood estimator for parametric and piecewise parametric trajectories. Even if good asymptotic properties hold, the non-robust behaviour of estimation is also described. The sensitivity of estimation is then studied when the state model is not completely specified. The cases of deterministic and stochastic state noise are considered in semiparametric frame when the law of state noise is unknown. In the last part, we consider the bearings-only tracking problem as a hidden Markov Model. We focus on the study of the optimal filter and on its approximation by algorithmic methods. The extended Kalman filter is tested under different state noise conditions. We finally give asymptotic stability results for non-ergodic hidden Markov models and their application to bearings-only tracking.
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https://tel.archives-ouvertes.fr/tel-00386071
Contributor : Benoît Landelle <>
Submitted on : Monday, July 6, 2009 - 11:07:22 AM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM
Long-term archiving on : Saturday, November 26, 2016 - 10:48:57 AM

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Benoit Landelle. Étude Statistique du Problème de la Trajectographie Passive. Mathématiques [math]. Université Paris Sud - Paris XI, 2009. Français. ⟨tel-00386071v4⟩

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