Local Ensemble Transform Kalman Filter: A non-stationary control law for complex adaptive optics systems on ELTs

We propose a new algorithm for an adaptive optics system control law which allows to reduce the computational burden in the case of an Extremely Large Telescope (ELT) and to deal with non-stationary behaviors of the turbulence. This approach, using Ensemble Transform Kalman Filter and localizations by domain decomposition is called the local ETKF: the pupil of the telescope is split up into various local domains and calculations for the update estimate of the turbulent phase on each domain are performed independently. This data assimilation scheme enables parallel computation of markedly less data during this update step. This adapts the Kalman Filter to large scale systems with a non-stationary turbulence model when the explicit storage and manipulation of extremely large covariance matrices are impossible. First simulation results are given in order to assess the theoretical analysis and to demonstrate the potentiality of this new control law for complex adaptive optics systems on ELTs.