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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 an N particle approximation with a asymptotic convergence. An application to nonlinear filtering for 3D atmospheric turbulent fluids will be described.
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 },
pages = {921--945},
publisher = {EDP-Sciences},
volume = {44},
number = {5},
year = {2010},
doi = {10.1051/m2an/2010047},
mrnumber = {2731398},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010047/}
}
TY - JOUR AU - Baehr, Christophe TI - Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2010 SP - 921 EP - 945 VL - 44 IS - 5 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010047/ DO - 10.1051/m2an/2010047 LA - en ID - M2AN_2010__44_5_921_0 ER -
%0 Journal Article %A Baehr, Christophe %T Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2010 %P 921-945 %V 44 %N 5 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010047/ %R 10.1051/m2an/2010047 %G en %F 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 , Special Issue on Probabilistic methods and their applications, Tome 44 (2010) no. 5, pp. 921-945. doi: 10.1051/m2an/2010047
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