An Identification Method for Stochastic Continuous-time Disturbances in Adaptive Optics Systems

This paper presents a novel identification method for stochastic continuous-time systems applied to Adaptive Optics. We consider a discrete-time sampled-data model of a linear combination of continuous-time second-order systems for modelling disturbances. The Maximum Likelihood framework is used in time and frequency domain to develop an estimation algorithm with sampled-data. We propose an estimation algorithm where we write the likelihood function in the frequency domain in terms of the discrete-time output spectrum (Whittle's log-likelihood function). An approximation for the discrete-time spectrum is used in order to reduce the computational load. A comparative analysis of the proposed method and some available methods is illustrated via numerical simulations.