Quantification of Uncertainty in Transfer function Estimation: A Mixed Deterministic-Probabilistic Approach

Abstract In this paper a procedure is presented to obtain an estimate of the transfer function of a linear system together with a confidence interval, using only limited a priori information. By applying Bartlett's procedure of periodogram averaging to the non-parametric empirical transfer function estimate, and by employing a periodic input signal, the statistics of the resulting estimate 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 a F distribution. For this analysis only minor assumptions are made on the distribution of the noise.