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Performance analysis of Kalman filter and minimum variance controllers for multi conjugate adaptive optics

In the framework of zonal approach for Multi Conjugate Adaptive Optics (multiple-mirror, multiple-guide star) we investigate a predictive Kalman Filter (KF) based controller and a non-predictive classical Minimum Variance (MV) algorithm. The main goal of this work is to compare phase estimation performance achievable by the computationally more expensive Kalman filter approach, which explicitly accounts for the atmospheric turbulence temporal behavior through a first order autoregressive evolution model, and a simpler MV algorithm with and without temporal prediction. For representative examples of the Palomar 5.1 meter telescope single conjugate and Gemini-South 8 meter telescope multi conjugate adaptive optics systems the performance of KF and MV controllers has been compared with respect to their turbulence estimation capability. We have found that the KF algorithm, showing superior performance for single conjugate adaptive optics systems, is less effective in multi conjugate case. It has also been shown that MV algorithm with a temporal prediction added to it can work nearly as good as KF.