Parameter Estimation of RBF-AR Model Based on the EM-EKF Algorithm

Abstract

RBF-AR (radial basis function network-based autoregressive) model is reconstructed as a new type of general radial basis function (RBF) neural network, which has additional linear output weight layer in comparison with the traditional three-layer RBF network. The extended Kalman filter (EKF) algorithm for RBF training has low filtering accuracy and divergence because of unknown prior knowledge, such as noise covariance and initial states. To overcome the drawback, the expectation maximization (EM) algorithm is used to estimate the covariance matrices of noises and the initial states. The proposed method, called the EM-EKF (expectation-maximization extended Kalman filter) algorithm, which combines the expectation maximization, extended Kalman filtering and smoothing process, is developed to estimate the parameters of the RBF-AR model, the initial conditions and the noise variances simultaneously. It is shown by the simulation tests that the EM-EKF method for the reconstructed RBF-AR network provides better results than structured nonlinear parameter optimization method (SNPOM) and the EKF, especially in low SNR (signal noise ratio). Moreover, the EM-EKF method can accurately estimate the noise variance. F test indicates there is significant difference between results obtained by the SNPOM and the EM-EKF.