An optimization procedure for a nonlinear system identification approach based on cubic splines

Nonlinear system identification is intended to model the nonlinear behavior of real-world devices. Among the state of the art, nonlinear modelling based on the Hammerstein cascade is a well-known and effective technique. The introduction in the model of an adaptive Catmull-Rom cubic spline and an adaptive FIR filter, also including a pre-processing for the system delay estimation, has been discussed in previous work. Therefore, starting from this result, an optimization procedure for the correct parametrization of this solution is presented in this paper based on the minimization of the mean square error chosen as fitness function. Several simulations were carried out in order to prove the effectiveness of the proposed solution in correctly setting the parameters of the adaptive algorithm. Tests were performed on a real electroacoustic device operating at different distortion level conditions. In particular, three main issues were taken into consideration, focusing first, on the validation of the optimization procedure, then, on the analysis of the sensitivity to the spline length, and finally, on the evaluation of the convergence parameters.