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 identificat ion scheme. This scheme identifies a polynomial Wiener system (linear FIR f ilter followed by a static polynomial nonlinearity) for noisy output observ ations. The analysis includes 1) bounds and a recursion for the misadjustme nt matrix and 2) algorithm mean square stability regions. A diagonal step-s ize matrix for the adaptive coefficients is introduced to speed up converge nce. The theoretical predictions of the fluctuation analysis are supported bg Monte Carlo simulations.