Generalized Extended Kalman Filter for Prediction of Chaotic Time-Series with Intermittent Failures

There are many practical situations in which the chaotic signal appears in the observation in a random manner so that there are intermittent failures in the observation mechanism at certain times. Using weights and network output of neural network as state equation and observation equation to obtain the linear state transition equation, and the chaotic time-series prediction results represented by the predicted observation value, this paper generalizes the extended Kalman filter (EKF) to the case for the prediction of chaotic time-series with intermittent observations when random interruptions in the observation process are modeled by a sequence of independent Bernoulli random variables. Finally, we test this scheme using simulated data based on the generalized EKF with different Bernoulli distribution probability for uncertain observations. Simulation results of Lorenz time-series prediction with synthetic data prove that the proposed algorithm in this paper has satisfactory prediction precision as well as good robustness.