Predict time series using extended, unscented, and cubature Kalman filters based on feed-forward neural network algorithm

Successful application of artificial neural networks (ANNs) in prediction of nonlinear systems with a high degree has made extensive studies in this field. Time-varying, dynamic properties, as well as internal noise, are the problems that occur in prediction of nonlinear systems. The advantages of nonlinear filtering algorithms are controlling the addictive noise and high accurate estimation during the implementation process. This paper explores the use of time-series forecasting algorithms by combining nonlinear filters with feedforward neural networks. In this paper, space state equations and measurement of non-linear filters are written based on the weights and output of the ANNs. In other word, the extended, unscented, and cubature Kalman filters is used for training the feed-forward neural network (FNN). To evaluate the proposed method, these techniques have been used to forecast Mackey-Glass time series. The overall accuracy of cubature Kalman filter is better than the two others. The results are also confirmed by computer simulations.