Nonlinear system identification with pseudorandom multilevel excitation sequences

The authors consider pseudorandom multilevel sequences (PRMS) for the identification of nonlinear systems modeled via a truncated Volterra series with a finite degree of nonlinearity and finite memory length. It is shown that PRMS are persistently exciting (PE) for a Volterra series model with nonlinearities of polynomial degree N if and only if the sequence takes on N+1 or more distinct levels. A computationally efficient least squares identification algorithm based on PRMS inputs is developed that avoids forming the inverse of the data matrix. Simulation results comparing identification accuracy using PRMS and Gaussian white noise are given.<>