Adaptive extended Kalman filter for online estimation of deformable mirror model parameters

For the final term paper for Rob Stengel’s graduate course in Optimal Control & Estimation, I wrote a MATLAB simulation to investigate applying a parameter-adaptive Kalman filter to the problem of wavefront control for high-contrast imaging. A deformable mirror model based on Gaussian influence functions was linearized with respect to the width of the Gaussian functions, and these widths were taken to be the model parameters adjustable by the adaptive filter. I simulated, in closed loop, the application of both a standard estimator as well as an adaptive estimator to a ground-based wavefront control system with Kolmogorov turbulence input and a phase conjugation control scheme; the goal of each routine was to drive the residual phase error to zero so as to create an image with high contrast. The residual error and image contrast were used as metrics to compare the two estimators, which ran for ten iterations of the control loop. The two estimators were shown to perform similarly, but this does not necessarily indicate the failure or infeasibility of parameter-adaptive estimation. Choosing the widths of the influence function as the adjustable parameters may not have been the best choice for the filter, as it is not clear whether variations in these parameters are observable in the phase error. A better choice may have been the influence function gains, and I intend to revisit these simulations at some point to try that instead.