Nonlinear Time Series Prediction Using Iterated Extended Kalman Filter Trained Single Multiplicative Neuron Model

摘要

Single Multiplicative Neuron (SMN) model is much simpler in structure than many other conventional Artificial Neural Networks (ANNs) and can offer better performances if properly trained, and dynamic filters have the advantage of being able to handle observations that change with time. In this paper we proposed an Iterated Extended Kalman Filter (IEKF) based SMN model for the prediction of nonlinear time series. The filter model is established by using the weights and biases of SMN to present the state vector and the output of SMN to present the observation equation, and the input vector to the SMN is composed of the known predicted values with given length. Different from traditional methods for time series prediction which split the predicted time series into training and test sets, the proposed approach is recursive and is well suited to on-line processing as a new observation arrived, and the whole prediction process is in a training state and can update the respective models from time to time. So the suggested technique can be suitable for the possible changes of system model. Finally, experiments on the predictions of Mackey-Glass time series, Box-Jenkins gas furnace data and Electroencephalogram (EEG) data are done and the results show that the IEKF-based SMN algorithm can achieve higher precision and better timeliness than that of previous study on the same data sets.