Abstract
A procedure is presented to obtain an estimate of the transfer function of a linear system together with an upper bound on the error, using only limited a priori information on the data generating process. By employing a periodic input signal, together with a non-parametric Emperical Transfer Function Estimate (ETFE) over each period, and by averaging over a number of estimates, the statistics of the resulting model asymptotically can be obtained from the data. The model error consists of two parts: a probabilistic part, due to the stochastic noise disturbance on the data, and a deterministic part, due to the bias in the estimate. The latter is explicitly bounded with a deterministic error bound, while the former asymptotically results from an F-distribution. For this analysis no assumptions are made on the distribution of the noise. A mixed deterministic-probabilistic error bound is achieved, clearly distinguishing the different sources of uncertainty.
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© 1994 Springer-Verlag
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de Vries, D.K., Van den Hof, P.M.J. (1994). A mixed deterministic-probabilistic approach for quantifying uncertainty in Transfer Function Estimation. In: Smith, R.S., Dahleh, M. (eds) The Modeling of Uncertainty in Control Systems. Lecture Notes in Control and Information Sciences, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036262
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DOI: https://doi.org/10.1007/BFb0036262
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