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To filter perturbed local measurements on a random medium, a dynamic model jointly with an observation transfer equation are needed. Some media given by PDE could have a local probabilistic representation by a Lagrangian stochastic process with mean-field interactions. In this case, we define the acquisition process of locally homogeneous medium along a random path by a Lagrangian Markov process conditioned to be in a domain following the path and conditioned to the observations. The nonlinear filtering for the mobile signal is therefore those of an acquisition process contaminated by random errors. This will provide a Feynman-Kac distribution flow for the conditional laws and a N particle approximation with a O( 1 p N ) asymptotic convergence. An application to nonlinear filtering for 3D atmospheric turbulent fluids will be described. Resume. Pour filtrer les mesures locales et perturbees d'un milieu aleatoire, un modele de dynamique et uneequation de transfert sont necessaires. Certains milieux decrits par une EDP peuvent avoir une representation probabiliste locale l'aide d'un processus stochastique Lagrangien en interaction avec un champ moyen. Dans ce cas, nous definissons le processus d'acquisition d'un milieu localement homogene le long d'un chemin aleatoire par un processus de Markov Lagrangien conditionnea vivre dans un domaine suivant le chemin et conditionne aux observations. Le filtrage non-lineaire du signal local est alors celui du processus d'acquisition bruite par des erreurs aleatoires. Ceci nous donne un flot de distribution de Feynman-Kac et une convergence asymptotique de l'approximation particulaires avec une erreur en O( 1 p N ). Une application au filtrage non-lineaire de fluides atmospherique 3D turbulent sera decrite.

Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities