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Estimation of the stochastic properties of controlled systems[editovat]

Author: Peter Matisko

Disertační práce 2013

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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.

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