Strong consistence of recursive identification for Wiener systems

The paper concerns identification of the Wiener system consisting of a linear subsystem followed by a static nonlinearity f (·) with no invertibility and structure assumption. Recursive estimates are given for coefficients of the linear subsystem and for the value f (v) at any fixed v. The main contribution of the paper consists in establishing convergence with probability one of the proposed algorithms to the true values. This probably is the first strong consistency result for this kind of Wiener systems. A numerical example is given, which justifies the theoretical analysis. 2005 Elsevier Ltd. All rights reserved.