Random and pseudorandom excitation sequences for nonlinear system identification

This paper considers random and pseudorandom excitation sequences for the identification of nonlinear systems modelled via a truncated Volterra series with a finite degree of nonlinearity and finite memory length. Random i.i.d. sequences are studied and necessary and sufficient conditions on the input that guarantee persistence of excitation are derived. The condition number of the correlation matrix corresponding to the Volterra series is mathematically characterized. A computationally efficient least squares identification algorithm based on i.i.d. excitation is developed. Simulations comparing identification accuracy using random and pseudorandom inputs are given.