On asymptotic frequency response variance expressions for estimated output error models

This papers concerns an extension of an asymptotic variance expression for Finite Impulse Response (FIR) model based frequency response estimation to the Output Error (OE) system identification case. It is based on the “useful input parametrization” for OE models, in which the Toeplitz covariance matrix structure instrumental in the FIR analysis is extended to OE model input representation after a Sylvester matrix transformation. We will use this result to derive a novel and transparent variance expression for the asymptotic OE frequency response estimate. This results simplifies the generalization of FIR results for optimal input design and cost of complexity system identification analysis to the OE case. Furthermore, the relation to previous exact variance error quantifications is explained.