Wednesday, November 27, 2019 - 14:00 in V3-201
On the continuous time limit of ensemble-based Kalman-type filtering algorithms
A talk in the Bielefeld Stochastic Afternoon series by
Theresa Lange from TU Berlin
| Abstract: |
Filtering algorithms aim at solving the problem of estimating the current
state of an unknown signal given noisy observations of that signal. For a
selection of ensemble-based Kalman-type filtering algorithms, this talk
will be concerned with the mathematically rigorous derivation of
continuous-time analogues of such algorithms. In the continuous-time
setting, we will apply these algorithms to the time-discretizations of the
underlying system and show that in the limit of decreasing discretization
stepsize the corresponding filter equations converge to an ensemble of
interacting (stochastic) differential equations in the
ensemble-mean-square sense. The analysis also allows for the derivation of
convergence rates with respect to the stepsize.
The resulting continuous time limit permits a better qualitative and
quantitative analysis of the discrete-time counterparts using the rich
theory of continuous-time dynamical systems.
|
Back
