Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 5, p. 921-945

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 N) asymptotic convergence. An application to nonlinear filtering for 3D atmospheric turbulent fluids will be described.

DOI : https://doi.org/10.1051/m2an/2010047
Classification:  82B31,  65C35,  65C05,  62M20,  60G57,  60J85
Keywords: nonlinear filtering, Feynman-Kac, stochastic model, turbulence
@article{M2AN_2010__44_5_921_0,
     author = {Baehr, Christophe},
     title = {Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {5},
     year = {2010},
     pages = {921-945},
     doi = {10.1051/m2an/2010047},
     zbl = {pre05798938},
     mrnumber = {2731398},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2010__44_5_921_0}
}
Baehr, Christophe. Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 5, pp. 921-945. doi : 10.1051/m2an/2010047. http://www.numdam.org/item/M2AN_2010__44_5_921_0/

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