Some peculiarities of identification in the presence of model errors

Abstract

Modelling errors are often the limiting factor in identification problems. Therefore, it is important to qualify their impact on the estimated plant model parameters θ̂(Z), where Z stands for the data. This paper qualifies the influence of model errors and disturbing noise level on: (i) the asymptotic value θ∗ (estimate for an infinite amount of data) of θ̂(Z), and (ii) the asymptotic (amount of data going to infinity) covariance matrix Cov(θ̂(Z)) of θ̂(Z). The theory is elaborated on a time- and frequency-domain estimator.