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

This correspondence investigates the statistical behavior of two adaptive gradient search algorithms for identifying an unknown Wiener–Hammerstein System (WHS) with Gaussian inputs. The first scheme attempts to identify the WHS with an LMS adaptive filter. The LMS algorithm identifies a scaled version of the convolution of the input and output linear filters of the WHS. The second scheme attempts to identify the unknown WHS with a gradient adaptive WHS when the shape of the nonlinearity is known a priori. The mean behavior of the gradient recursions are analyzed when the WHS nonlinearity is modeled by an error function. The mean recursions yield very good agreement with Monte Carlo simulations for slow learning.