GEKF, GUKF and GGPF based prediction of chaotic time-series with additive and multiplicative noises

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.     

Generalized unscented Kalman filtering based radial basis function neural network for the prediction of ground radioactivity time series with missing data

On the assumption that random interruptions in the observation process are modeled by a sequence of independent Bernoulli random variables, we firstly generalize two kinds of nonlinear filtering methods with random interruption failures in the observation based on the extended Kalman filtering (EKF) and the unscented Kalman filtering (UKF), which were shortened as GEKF and GUKF in this paper, respectively. Then the nonlinear filtering model is established by using the radial basis function neural network (RBFNN) prototypes and the network weights as state equation and the output of RBFNN to present the observation equation. Finally, we take the filtering problem under missing observed data as a special case of nonlinear filtering with random intermittent failures by setting each missing data to be zero without needing to pre-estimate the missing data, and use the GEKF-based RBFNN and the GUKF-based RBFNN to predict the ground radioactivity time series with missing data. Experimental results demonstrate that the prediction results of GUKF-based RBFNN accord well with the real ground radioactivity time series while the prediction results of GEKF-based RBFNN are divergent.