An optimal recovery formulation of data assimilation in haemodynamics
Résumé
An optimal formulation of a state estimation problem is introduced, which can be considered as a modification of the Parametrised Background Data Weak method. Several results and numerical experiments are proposed. In the second part, the problem of the definition of an optimal recovery method for a dynamical data assimilation problem is considered. A Tensor Train approximation of the set of parametric solutions is considered, which makes it possible to get an observability estimation. This can be considered as the counterpart, for the dynamical optimal recovery, of the Kalman observability criterion for LTI systems.