On numerically reliable frequency-domain system identification: new connections and a comparison of methods

Frequency domain identification of complex systems imposes important challenges with respect to numerically reliable algorithms. This is evidenced by the use of different rational and data-dependent basis functions in the literature. The aim of this paper is to compare these different methods and to establish new connections. This leads to two new identification algorithms. The conditioning and convergence properties of the considered methods are investigated on simulated and experimental data. The results reveal interesting convergence differences between (nonlinear) least squares and instrumental variable methods. In addition, the results shed light on the conditioning associated with so-called frequency localising basis functions, vector fitting algorithms, and (bi)-orthonormal basis functions.