Stochastic analysis of adaptive gradient identification of Wiener-Hammerstein systems for Gaussian inputs

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.