This paper presents analytical and Monte Carlo results for a stochastic gra
dient adaptive scheme that tracks a time varying polynomial Wiener system [
i.e., a linear time-invariant (LTI) filter with memory followed by a time-v
arying memoryless polynomial nonlinearity], The adaptive scheme consists of
two phases: 1) estimation of the LTI memory using the LMS algorithm and 2)
tracking the time-varying polynomial-type nonlinearity using a second coup
led gradient search for the polynomial coefficients. The time varying polyn
omial nonlinearity causes a time-varying scaling; for the optimum Wiener fi
lter for Phase 1, These time variations are removed for Phase 2 using a nov
el coupling scheme to Phase I. The analysis for Gaussian data includes recu
rsions for the mean behavior of the I,RIS algorithm for estimating and trac
king the optimum Wiener filter for Phase 1 for several different time-varyi
ng polynomial nonlinearities and recursions for the mean behavior of the st
ochastic gradient algorithm for Phase 2, The polynomial coefficients are sh
own to be accurately tracked, Monte Carlo simulations confirm the theoretic
al predictions and support the underlying statistical assumptions.