Frequency localising basis functions for wide-band system identification: A condition number bound for Output Error systems

Identifying the parameters of a system possessing a large dynamic range presents a number of difficulties for a least squares type algorithm. Foremost, is that of obtaining reliable parameter estimates from a poor or ill-conditioned least squares formulation. In this paper we examine properties of a technique that utilises frequency localising basis functions to ensure that ill-conditioning is reduced when solving for the parameter estimates. Specifically, we obtain a bound on the condition number of the least squares problem which is independent of the frequency range for a particular class of models. We also present an example, utilising real data, which demonstrates the potential of the technique when applied to large dynamic range systems.