Nj. Bershad et al., Stochastic analysis of adaptive gradient identification of Wiener-Hammerstein systems for Gaussian inputs, IEEE SIGNAL, 48(2), 2000, pp. 557-560
This correspondence investigates the statistical behavior of two adaptive g
radient search algorithms for identifying an unknown Wiener-Hammerstein Sys
tem (WHS) with Gaussian inputs. The first scheme attempts to identify the W
HS with an LMS adaptive filter. The LMS algorithm identifies a scaled versi
on of the convolution of the input and output linear filters of the WHS. Th
e second scheme attempts to identify the unknown WHS with a gradient adapti
ve WHS when the shape of the nonlinearity is known a priori. The mean behav
ior of the gradient recursions are analyzed when the WHS nonlinearity is mo
deled by an error function. The mean recursions yield very good agreement w
ith Monte Carlo simulations for slow learning.