CONVERGENCE ANALYSIS OF RECURSIVE-IDENTIFICATION ALGORITHMS BASED ON THE NONLINEAR WIENER MODEL

Recursive identification algorithms, based on the nonlinear Wiener mod el, are presented in this paper. A recursive identification algorithm is first derived from a general parameterization of the Wiener model, using a stochastic approximation framework. Local and global convergen ce of this algorithm can be tied to the stability properties of an ass ociated differential equation. Since inversion is not utilized, noninv ertible static nonlinearities can be handled, which allows a treatment of, for example, saturating sensors and blind adaptation problems. Ga uss-Newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single-inpu t/single-output case. The proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbanc es affect the output signal. For FIR (finite impulse response) models, it is also proved that global convergence of the schemes is tied to s ector conditions on the static nonlinearity. In particular, global con vergence of the stochastic gradient method is obtained, provided that the nonlinearity is strictly monotone. The local analysis, performed f or IIR (infinite impulse response) models, illustrates the importance of the amplitude contents of the exciting signals.