Prediction of Chaotic Time Series Based on Neural Network with Legendre Polynomials

In this paper, a modeling method based on the orthogonal function neural network is proposed. Legendre orthogonal polynomials are selected as the basic functions of the neural network. Kalman filtering algorithm with singular value decomposition is used to confirm the parameters of orthogonal function neural network in order to avoid error delivery and error accumulation. To demonstrate the performance of this modeling method, the simulation on Mackey-Glass chaotic time series is performed. The results show that this method provides effective and accurate prediction.