Online chaotic time-series prediction with the derivative-free extended Kalman filter

Derivative-free extended Kalman filter (DEKF) represented uncertainty by an ensemble set of state vectors rather than by the traditional mean and covariance measures, avoiding the need for the calculation of Jacobian matrices. This paper used weights and network output of multilayer perceptron as state equation and measurement equation to obtain the linear state transition equation, and the prediction results of chaotic time-series were represented by the predicted measurement value, which was different from the previous filtering methods based chaotic time-series prediction, an efficient algorithm was suggested for chaotic time-series prediction scheme. Finally, we test this scheme using simulated data based on the extended Kalman filtering (EKF) and DEKF, respectively. Simulation results of EKF and DEKF based Mackey-Glass time-series prediction with synthetic data prove that the prediction accuracy of DEKF is close to EKF as parameter α tends to some value, but the run time of DEKF is much longer than EKF.