Fast finite-horizon kalman filter in wavefront estimation for adaptive optics

We consider the problem of wavefront estimation for the control of adaptive optics systems. It has been shown that an improvement in the performance can be achieved by assuming a turbulence dynamical model which allows the use of a Kalman filter; nevertheless, the implementation of such filters has proven to be difficult in real-time large-scale systems due to memory, computational costs and latency issues. In this article we propose a possible work around of such problem, which consists in using the non-recursive expression of a finite-horizon Kalman filter, which only requires a matrix-vector multiplication at run-time. This allows the use of complex state-space models for the estimation, without the need of explicitly computing the state vector at each time step, yielding a significant gain in term of computational time.