Online identification of the ARX model expansion on Laguerre orthonormal bases with filters on model input and output
Résumé
This paper proposes a new representation of ARX models on independent and orthonormal Laguerre bases by filtering the process input and output using Laguerre orthonormal functions. The resulting model titled ARXLaguerre model ensures the parameter number reduction with a recursive and easy representation. However this reduction still subject to an optimal choice of the Laguerre pole of each Laguerre basis. Therefore, we propose an analytical solution to optimize Laguerre poles which depend on Fourier coefficients defining the ARX-Laguerre model and that are identified using the regularized square error. The identification of Laguerre pole and Fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the ARX-