System identification using Laguerre models

The traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear-in-the-parameters predictor models leads to approximations of very high order in cases of rapid sampling and/or dispersion in time constants. By using prior information about the time constants of the system more appropriate expansions, related to Laguerre networks, are introduced and analyzed. It is shown that the model order can be reduced, compared to ARX (FIR, AR) modeling, by using Laguerre models. Furthermore, the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the Laguerre parameter. Consistency (error bounds), persistence of excitation conditions. and asymptotic statistical properties are investigated. This analysis is based on the result that the covariance matrix of the regression vector of a Laguerre model has a Toeplitz structure