NONLINEAR FILTERING WITH CONVOLUTION KERNELS APPLICATION
TO A PROCESS OF BIOLOGICAL DEPOLLUTION
Abstract:
This thesis considers the problem of nonlinear filtering, i.e. the on
line estimation of the indirectly observed state of a nonlinear
dynamical system. This type of problems relates to a broad range of
models relative to various scientific fields. An original approach
using the convolution kernels and simulations of a large number of
random variables is developed. The case of the models with unknown
parameters to estimate is also treated. Theoretical properties of
convergence are established for these new approaches. In order to
complete the study of our techniques, the comparisons with the
traditional methods, especially with the various particle filters, are
carried out in simulation. Then our new approaches are applied to a
real problem, a bioreactor for wastewater treatment. The performances
obtained, on real data, make it possible to appreciate the robustness
of the method with respect to the model errors and perturbated data.
MM. P. DEL
MORAL
Professor University of
Nice
L. DEVROYE Professor
Mc Gill University
(Reviewer)
G. DUCHARME Professor
University of
Montpellier II
F. LEGLAND Dir. de
recherche IRISA/INRIA
Rennes
(Reviewer)
B. PORTIER Maitre de
Conf. University
of Paris-Sud
G.
TRYSTRAM Professor
ENSIA Massy
(Reviewer)
J.P. STEYER Dir. de
recherche INRA
Narbonne
J.P.
VILA Dir. de recherche INRA
Montpellier (Advisor)