Fluctuation analysis of stochastic gradient identification of polynomial Wiener systems

This correspondence presents analytical results and Monte Carlo simulations for the fluctuation behavior of a stochastic gradient adaptive identification scheme. This scheme identifies a polynomial Wiener system (linear FIR filter followed by a static polynomial nonlinearity) for noisy output observations. The analysis includes (1) bounds and a recursion for the misadjustment matrix and (2) algorithm mean square stability regions. A diagonal step-size matrix for the adaptive coefficients is introduced to speed up convergence. The theoretical predictions of the fluctuation analysis are supported by Monte Carlo simulations.