Nonlinear system identification by means of mixtures of linear-in-the-parameters nonlinear filters

In this paper, we deal with the unconstrained linear combination of the outputs of linear-in-the-parameters (LIP) nonlinear filters. We first analyze its steady-state performance using the Wiener theory of the optimal filter. Then, the implementation of the mixture of a linear and an even mirror Fourier nonlinear filter is considered. A simple adaptation algorithm for the filters in the mixture scheme that does not require the preliminary choice of the step sizes, as in the case of usual adaptation algorithms, is proposed. The presented approach is useful for the identification of time-varying nonlinear systems, exploiting the orthogonality of the basis functions of the constituent filters in presence of a white uniform input signal in [-1, +1]. Simulations results are reported showing the good performance obtained in these cases.