Nonlinear time series prediction using wavelet networks with Kalman filter based algorithm

The idea of combining both wavelets and neural networks has resulted in the formulation of wavelet networks, whose basic functions are drawn from family of orthonormal wavelets. The usual method to train wavelet networks is the backpropagation algorithm described by Rumelhart et al. However, this algorithm converges slowly for large or complex problems such as speech recognition, where more than thousands of iterations may be needed for convergence, even with small data sets. In this paper, we propose to train wavelet network for nonlinear time series prediction using the unscented Kalman filter (UKF), which needs less iterations than backpropagation algorithm. UKF is a powerful nonlinear estimation technique and has been shown to be a superior alternative to the extended Kalman filter (EKF) in a variety of applications, including parameter estimation for time series modeling and neural network training. Several simulation results are presented to validate the proposed method