Random versus pseudorandom test signals in nonlinear-system identification

The crosscorrelation method of nonlinear-system identification, by use of quasiwhite test signals, is one of the most powerful approaches to the black-box identification problem. The increasing popularity of the method in applications of physical and physiological systems has raised the question of optimality in the selection of the appropriate quasiwhite test signal. Two families of quasiwhite signals pose as principal candidates in this selection process: the pseudorandom signals based on m-sequences (p.r.s.) and the constant-switching-pace symmetric random signals (c.s.r.s.). The paper investigates the question of relative merit of these two families, by summarising the main theoretical findings concerning their properties and by presenting two examples which illustrate their relative accuracy in kernel estimation and model prediction. The main point, which is demonstrated in this study, is that the accuracy of models of nonlinear systems estimated by use of c.s.r.s. is higher, even though p.r.s. give better estimates in the case of linear-system identification.