Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities
Météo-France-CNRS, CNRM-GAME URA1357, 42 avenue Coriolis, 31057 Toulouse Cedex 1, France. email@example.com
2 Associated member of the Laboratory of Statistics and Probability of the Toulouse Mathematics Institute (UMR 5219), 118 route de Narbonne, 31062 Toulouse Cedex 9, France.
Revised: 23 December 2009
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 an N particle approximation with a asymptotic convergence. An application to nonlinear filtering for 3D atmospheric turbulent fluids will be described.
Mathematics Subject Classification: 82B31 / 65C35 / 65C05 / 62M20 / 60G57 / 60J85
Key words: Nonlinear filtering / Feynman-Kac / stochastic model / turbulence
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