Nonlinear system identification using Wiener type Laguerre–Wavelet network model

Compact nonlinear black box models, capable of representing highly nonlinear systems, are of high demand both in industry and academia. In this paper it has been shown that the use of Laguerre basis filters coupled with a wavelet network in Wiener type model structure are capable of modeling highly nonlinear systems with acceptable accuracy. Although individual merits of orthonormal basis functions (especially Laguerre filters) and multiresolution wavelet decompositions and/or wavelet network have been well documented in various literatures on system identification in the past, their combinational advantages in nonlinear system identification has never been explored. Laguerre filter models have the ability to approximate linear systems (even with time delay) with a model order lower than the traditional ARX (e.g., FIR, AR) modeling. Use of Laguerre models for mildly nonlinear system is possible only with a piece-wise linear models. Wavelet basis functions have the property of localization in both time and frequency and they can approximate even severe nonlinearities with appreciable accuracy with fewer model terms. But wavelet approximations fail miserably, in terms of model parsimony, if used for approximating linear or mildly nonlinear systems. In the present work a Laguerre–Wavelet network model has been proposed which combines the Laguerre and Wavelet approximations. In the said model, merits of both these approximations are retained whereas their demerits are suppressed.