System identification using high-order models, revisited

The traditional approach of expanding transfer functions and noise models in the delay operator to obtain predictor models linear in the parameters leads to approximations of very high order in the case of rapid sampling and/or large dispersion in time constants. By using a priori information about the time constants of the system, more appropriate expansions, closely related to Laguerre networks, are introduced and analyzed. It is shown that these expansions need much lower orders to obtain reasonable approximations and improve the numerical properties of the estimation algorithm. Consistency (error bounds), persistence of excitation conditions, and asymptotic statistical properties are investigated