Fast nonlinear adaptive filtering using a partial window conjugate gradient algorithm

In this paper a modified form of the partial conjugate gradient algorithm is presented for use in nonlinear filtering using neural networks. The algorithm is based on using a gradient average window to provide a trade-off between convergence rate and complexity which, depending on the choice of averaging window, is (in both complexity and speed of convergence) intermediate between the conventional backpropagation (BP) algorithm and the Newton methods. An additional simplification is introduced by replacing the calculated optimum step size α_k by a normalized step size α¯, in the same manner as the normalized LMS algorithm. This new algorithm is applied to a cascaded neural network/nonlinear least mean squares structure for the identification of a nonlinear system. This proposed algorithm demonstrates improved convergence rates with even small choices of window size