An improved EKF based neural network training algorithm for the identification of chaotic systems driven by time series

This paper presents a novel algorithm for nonlinear system identification from a single channel output time series of a chaotic signal. A recurrent neural network(RNN) structure has been designed to represent the non linear system. The neural network weights are estimated using the Extended Kalman Filter(EKF) algorithm, augmented by the Expectation Maximization(EM) algorithm used to derive the initial states and covariance, of the Kalman filter. Rossler chaotic system is used for demonstration of the approach. The simulation results show that the Artificial Neural Network(ANN) trained with EKF algorithm, as outlined above, performs with an appreciably low value of modeling error, and give exact reproduction of the output time series and states, as generated from the dynamical equations. The Lyapunov exponents of the model are calculated, from the state space evolution, which confirms the chaotic behaviour.