  Many nonlinear systems can be described by a Wiener-Schetzen model. In this
model, the linear dynamics are formulated in terms of orthonormal basis
functions (OBFs). The nonlinearity is modeled by a multivariate polynomial. In
general, an infinite number of OBFs is needed for an exact representation of
the system. This paper considers the approximation of a Wiener system with
finite-order infinite impulse response dynamics and a polynomial nonlinearity.
We propose to use a limited number of generalized OBFs (GOBFs). The pole
locations, needed to construct the GOBFs, are estimated via the best linear
approximation of the system. The coefficients of the multivariate polynomial
are determined with a linear regression. This paper provides a convergence
analysis for the proposed identification scheme. It is shown that the estimated
output converges in probability to the exact output. Fast convergence rates, in
the order $O_p({N_F}^{-n_{rep}/2})$, can be achieved, with $N_F$ the number of
excited frequencies and $n_{rep}$ the number of repetitions of the GOBFs.
