System identification from measured signals

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Dr. Kollár István
Department of Measurement and Information Systems

The subject of this paper is parameter estimation and frequency domain model estimation in case of measurement signals with random components or noise. The examined method leads to the statistically possible most accurate value. The first part is a recapitulation of probability theory basics and the most common probability density functions. It introduces the Fisher score and the Fisher information matrix for the mentioned density functions. The attainable precision is described by the theory of the Cramér-rao bound and it will also be proven that this bound can be reached with the maximum likelihood estimator if the covariance matrix is known. After all, the unbiased maximum likelihood estimator will be introduced for normally distributed observations. In the second part of the paper frequency domain models and the adaption of the estimator will be discussed. The inaccuracy of the measurements and a possible solution with model parameter estimation is shown through a simple example.


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