Natural gradient learning neural networks for adaptive inversion of Hammerstein systems

This letter applies natural gradient (NG) learning neural networks for adaptive inversion of Hammerstein systems. The system model is composed of a memoryless nonlinearity g(.) followed by a linear filter H. The inverse system is modeled by a neural network composed of an adaptive filter Q followed by a memoryless nonlinear perceptron. The adaptive filter Q aims at inverting the linear part of the system (adaptive deconvolution). The perceptron aims at inverting the memoryless function (adaptive function inversion). The adaptive system is trained using the NG descent algorithm. The letter shows through computer simulations that the NG approach outperforms the classical backpropagation algorithm in terms of mean-squared-error performance and convergence speed.