Modeling and identification of adaptive optics systems to satisfy distributed Kalman filter model structural constraints

Turbulence estimation in ground based telescopes as part of the Adaptive Optics (AO) control loop is inherently high-complexity. Even in smaller telescopes such as the EOS 1.8m telescope at Mt Stromlo Observatory, Canberra, closed-loop control systems are required to operate in the order of kHz with hundreds, if not thousands of internal states. Typical Matrix Vector Multiply (MVM) control calculations grow in computational demand to the order of N2. The Distributed Kalman Filter (DKF) proposed by Massioni et al [1] when being performed in the Fourier Domain allows the computational cost to scale as N log N [2], provided that the state space model is shift-invariant in its basis. In this paper we develop a procedure for the modeling and identification of a dynamic shift-invariant turbulence model that does not require prior knowledge of the layers velocities and turbulence profile, while satisfying the structural requirements of the DKF.