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Thèmes de recherche
By studying the measurements made with a mobile sensor in a random medium, we have defined and give the properties of the acquisition process of a vector field along a random path. For the stochastic filtering of the conditioned acquisition process, we have proposed new algorithms of non-linear filtering for mean-field processes and for some various types of laws. We prove the convergence of the particle approximation for each new algorithms of estimates we gave. The resulted filtering algorithms are based on the dynamics of genealogical trees where the processes interact by genetic selections and by their mean-field law.
This innovative work allowed us to filter velocity measurements of a turbulent fluid. We present several applications of our methods by using some 1D, 2D or 3D measurements, simulated or real. Our techniques make it possible to obtain high frequency estimates of the fluid velocities as well as quantities characterizing turbulence, and we proceed to a systematic study on numerical errors produced by our methods of calculation. Some applications for doppler LIDAR measurements have been achieved.
The second part of our research is linked to data assimilation. We study different non-linear techniques used in stochastic engineering to suggest new algorithms appropriate to high dimensional problems occuring in atmospheric data assimilation. In the end, we study the mathematical properties of this new estimators. This work shape a convergence between resampling particle filters and corrective variational assimilation.
This new field of research give also a coherent frame to assimilate properly new instruments using their own capabilites to explore the turbulence.
Publications
Publications avec comités de lecture
C. Baehr (2010) : Nonlinear Filtering for observations on a random vector field along a random path. M2AN – ESAIM 2010, 44 (5), 921-945, DOI No : 10.1051/m2an/2010047
M. Lei, P. Del Moral and C. Baehr (2009) : Fisher Information Matrix-based Nonlinear System Conversion for State Estimation. IEEE transaction on Control and Automation, 06/2010, 837-841, DOI No : 10.1109/ICCA.2010.5524066.
M. Lei, P. Del Moral and C. Baehr (2009) : Analysis of Approximated PCRLBs for Nonlinear Dynamics Using Different Moments of State Estimate. IEEE transaction on Control and Automation 06/2010, 1988-1993, DOI No : 10.1109/ICCA.2010.5524070.
C. Baehr (2009) : Stochastic modeling and filtering of discrete measurements for a turbulent field. application to measurements of atmospheric wind. Int. Journal Modern Phys. B, 23 (28-29), 5424-5433, DOI No : 10.1142/S0217979209063742
Rapports / livres
O. Pannekoucke and C. Baehr (2010) : Kalman filters family in geoscience and beyond chapter in Kalman Filtering. J.M. Gomez Ed. Nova Science Publishers, 2010
C. Baehr and O. Pannekoucke (2009) : Some issues and results on the EnKF and particle filters for meteorological models. chapter in Chaotic Systems : Theory and Applications., 27-34. DOI No : 10.1142/9789814299725_0004. C. H. Skiadas and I. Dimotikalis Ed. World Scientific, 2010
Enseignement
Master 2 Biostatistique et Modélisation : Traitement du Signal Aléatoire
Master 1 Ecologie Aquatique : Introduction à l’étude des séries chronologiques
Météo-France Cours Élève Ingénieur de la Météorologie : Traitement du Signal Déterministe et Aléatoire
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