  Stabilization, disturbance rejection, and control of optical beams and
optical spots are ubiquitous problems that are crucial for the development of
optical systems for ground and space telescopes, free-space optical
communication terminals, precise beam steering systems, and other types of
optical systems. High-performance disturbance rejection and control of optical
spots require the development of disturbance estimation and data-driven Kalman
filter methods. Motivated by this, we propose a unified and experimentally
verified data-driven framework for optical-spot disturbance modeling and tuning
of covariance matrices of Kalman filters. Our approach is based on covariance
estimation, nonlinear optimization, and subspace identification methods. Also,
we use spectral factorization methods to emulate optical-spot disturbances with
a desired power spectral density in an optical laboratory environment. We test
the effectiveness of the proposed approaches on an experimental setup
consisting of a piezo tip-tilt mirror, piezo linear actuator, and a CMOS
camera.
