An optimal and unifying vector fitting method for frequency-domain system identification

This paper proposes an optimal and unifying instrumental variable (IV)-based Vector Fitting (VF) method for frequency-domain (FD) identification of models formed by rational basis function (RBF) expansions. The proposed method is denoted by IV-FD-VF and can be similarly applied for estimating models formed by both continuous- and discrete-time RBF sets. The key advantage of IV-FD-VF lies in the fact that, differently from standard FD-VF approaches, it guarantees an optimal solution after convergence. This important optimality property is proved to be independent of the nature of the noise that corrupts the data (for instance, if it is white or coloured). Two case studies are used to validate the proposed IV-FD-VF method. One of these case studies considers actual frequency-domain data sets extracted from two different single-phase power transformers.