Abstract On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering (EKF), the unscented Kalman filtering (UKF) and the Gaussian particle filtering (GPF) to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal (These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper). Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey--Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.
Received: 05 November 2007
Revised: 01 December 2007
Accepted manuscript online:
Fund: Project supported by
the National Natural Science Foundation of China (Grant No 60774067)
and the Natural Science Foundation of
Fujian Province of China (Grant No 2006J0017).
Cite this article:
Wu Xue-Dong(伍雪冬) and Song Zhi-Huan(宋执环) GEKF, GUKF and GGPF based prediction of chaotic time-series with additive and multiplicative noises 2008 Chin. Phys. B 17 3241
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