NONLINEAR FILTERING FOR OBSERVATIONS ON A RANDOM VECTOR FIELD ALONG A RANDOM PATH. APPLICATION TO ATMOSPHERIC TURBULENT VELOCITIES

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 O(1/root N) asymptotic convergence. An application to nonlinear filtering for 3D atmospheric turbulent fluids will be described.