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

Christophe Baehr

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 5, page 921-945
  • ISSN: 0764-583X

Abstract

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

How to cite

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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 44.5 (2010): 921-945. <http://eudml.org/doc/250811>.

@article{Baehr2010,
abstract = { 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 $\mathcal\{O\}$$(\frac\{1\}\{\sqrt\{N\}\})$ asymptotic convergence. An application to nonlinear filtering for 3D atmospheric turbulent fluids will be described. },
author = {Baehr, Christophe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonlinear filtering; Feynman-Kac; stochastic model; turbulence; nonlinear filtering},
language = {eng},
month = {8},
number = {5},
pages = {921-945},
publisher = {EDP Sciences},
title = {Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities},
url = {http://eudml.org/doc/250811},
volume = {44},
year = {2010},
}

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
DA - 2010/8//
PB - EDP Sciences
VL - 44
IS - 5
SP - 921
EP - 945
AB - 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 $\mathcal{O}$$(\frac{1}{\sqrt{N}})$ asymptotic convergence. An application to nonlinear filtering for 3D atmospheric turbulent fluids will be described.
LA - eng
KW - Nonlinear filtering; Feynman-Kac; stochastic model; turbulence; nonlinear filtering
UR - http://eudml.org/doc/250811
ER -

References

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