RANDOM AND PSEUDORANDOM INPUTS FOR VOLTERRA FILTER IDENTIFICATION

This paper studies input signals for the identification of nonlinear d iscrete-time systems modeled via a truncated Volterra series represent ation. A Kronecker product representation of the truncated Volterra se ries is used to study the persistence of excitation (PE) conditions fo r this model. It is shown that i.i.d. sequences and deterministic pseu dorandom multilevel sequences (PRMS's) are PE for a truncated Volterra series with nonlinearities of polynomial degree N if and only if the sequences take on N + 1 or more distinct levels. It is well known that polynomial regression models, such as the Volterra series, suffer fro m severe ill-conditioning if the degree of the polynomial is large. Th e condition number of the data matrix corresponding to the truncated V olterra series, for both PRMS and i.i.d. inputs, is characterized in t erms of the system memory length and order of nonlinearity. Hence, the trade-off between model complexity and ill-conditioning is described mathematically. A computationally efficient least squares identificati on algorithm based on PRMS or i.i.d. inputs is developed that avoids d irectly computing the inverse of the correlation matrix. In many appli cations, short data records are used in which case it is demonstrated that Volterra filter identification is much more accurate using PRMS i nputs rather than Gaussian white noise inputs.