Uncertainty of transfer function modelling using prior estimated noise models

Abstract

Assuming “small” model errors (unmodelled dynamics and/or nonlinear distortions) and “large” signal-to-noise ratios we derive in this paper explicit expressions for the covariance matrix of a frequency domain estimator using prior estimated noise models. These analytic expressions (i) give a clear insight in the behaviour of the covariance matrix as a function of the signal-to-noise ratio, the unmodelled dynamics and the nonlinear distortions, and (ii) allow to predict accurately the order of magnitude of the actual uncertainty of the estimates. The link with the classical prediction error approach is also established.