Ensemble Transform Kalman Filter, a nonstationary control law for complex AO systems on ELTs: theoretical aspects and first simulations results

Optimal control laws for new Adaptive Optics (AO) concepts in astronomy require the implementation of techniques intended for real time identification of the atmospheric turbulence. Contrary to the Optimized Modal Gain Integrator (OMGI), it has been proved that the Kalman Filter (KF) based optimal control law enables estimation and prediction of the turbulent phase from the measurements and corrects efficiently the different modes of this phase in the case of a wide field tomographic AO system. But using such kind of processes, for any Extremely Large Telescope (ELT), will be extremely difficult because of the numerical complexity of the computations involved in the matrices calculations as well as the recording of large covariance matrices. A new control law is proposed, based on the Ensemble Transform Kalman Filter (ETKF) and its efficient variation, Local ETKF (recently developed for geophysics applications), allowing to dramatically reduce the computation burden for an ELT implementation and also to deal with non stationary behaviors of the turbulence.

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