Evaluation of statistical turbulence models for use in the Distributed Kalman Filter

The Kalman Filter (KF) application to wavefront control in Adaptive Optics (AO) shows great promise with respect to achieving the best atmospheric turbulence error rejection, provided an adequate model for the turbulence temporal dynamics exists. The advent of the computationally efficient Distributed Kalman Filter (DKF) algorithm makes the KF approach especially attractive for the future of high DOF AO systems (As is the case in the Extremely Large Telescope class). In this work we try to address a significant drawback of the existing DKF state space model, which is too simplistic (single parameter scalar diagonal state matrix) to describe the atmosphere turbulence dynamics. We investigate a broader family of Block-Toeplitz with Toeplitz Blocks (BTTB) state matrices, which, on one hand, are able to better grasp statistical properties of the turbulence to provide significantly better prediction power and, on the other hand, preserve the shift invariance property, a corner stone of the DKF algorithm. We demonstrate the capabilities of the new model in the end-to-end simulations of the DKF-driven Single Conjugate AO system.