Identification of the bilinear-Laguerre model on a sliding window

In this paper, we propose a new nonlinear representation by expanding discrete-time bilinear model on Laguerre orthonormal bases. Thus the coefficients associated to the input, to the output and to the crossed product of the bilinear model are expanded on three independent Laguerre bases. Compared to classical bilinear model, the resulting model entitled bilinear-Laguerre model ensures a significant parameter number reduction as well as simple recursive representation. However, this reduction is still subject to an optimal choice of the Laguerre poles defining the Laguerre bases. Therefore, we propose an analytical solution to optimize the Laguerre poles which depend on Fourier coefficients defining the bilinear-Laguerre model, and that are identified using the RLS method. The identification procedures of the Laguerre poles and Fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the bilinear-Laguerre model. The bilinear-Laguerre model as well as the proposed algorithm are illustrated and tested on numerical simulation.