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Estimation of the stochastic properties of controlled systems
Author: Peter Matisko
The doctoral thesis covers a part of the stochastic properties identification for linear dynamic systems.
Knowledge of the noise sources and uncertainties is essential for the state estimation performance. The
covariances of the process and measurement noise represent tuning parameters for the Kalman filter
and the state estimation quality depends directly on them. The thesis deals with estimation of the noise
covariances from the measured data. A Bayesian approach together with Monte Carlo methods are
employed for this task. The thesis describes optimality tests that can be used to evaluate the quality of
the state estimates obtained by a Kalman filter. A new approach was introduced to detect the color
property of the process noise. If the process noise is colored, the shaping filter can be found in the time
or frequency domain. It can be added to the Kalman filter which can be then tuned optimally. The
limitations of the noise covariance estimation are evaluated by the Cramér–Rao bounds. The
convergence of the proposed algorithms and the previously published ones were compared.
- Peter Matisko, mailto:p.matisko@gmail.com