On Frequency-Domain Identification of Linear Systems

The maximum-likelihood estimation of the parameters of linear systems and the properties of the estimator (Estimator for Linear Systems, ELiS) have been described in a paper by R. Pintelon and J. Schoukens (“Robust identification of transfer functions in sand z-domain,” IEEE TRANSACTIONS Aug. 1990). The mathematics used in the development of the method and the proofs are rather involved. However, several statements can be understood in heuristic terms. This paper discusses the complex-domain description of the method, which results in much simpler expressions. The method is also compared to other formations, giving more insight into the properties of the estimate. It turns out that robustness is at least partly due to the least-squares formulation. Derivations are avoided where possible, and intuitive explanations are given instead. ON INSTRUMENTATION AND MEASUREMENT, Vol. 39, pp. 565-573,