Quantification of frequency domain error bounds with guaranteed confidence level in prediction error identification

This paper considers prediction error identification of linearly parametrized models in the situation where the system is in the model set. For such situation it is easy to construct a confidence ellipsoid in parameter space in which the true parameter lies with an a priori fixed probability level, α. Surprisingly perhaps, the construction of a corresponding uncertainty set in the frequency domain, to which the true system belongs with probability α, is still an open problem. We show in this paper how to construct such frequency domain uncertainty set with a probability level of at least α.