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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topBaehr, 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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