Nonlinear time series online prediction using reservoir kalman filter

A novel online adaptive prediction method is proposed for complex time series. The KF is adopted in the high-dimension ldquoreservoirrdquo state space and directly updates the output weights of the echo state network (ESN) online. Compared with the expanded Kalman filter (EKF) algorithm of traditional recurrent neural networks, the reservoir KF method offers a implementation without the computation of numerical derivatives, so as to improve the prediction accuracy and extend the applications. Stability and convergence analysis of the proposed method is presented. Simulation examples demonstrate the validity of the proposed method.