基于EM-EKF算法的RBF-AR模型参数估计

为了利用EKF（extended Kalman filter）算法对RBF-AR（radial basis function network-based autoregressive）模型进行参数估计，重构了RBF-AR模型的网络结构，将其变换成一种新型的广义径向基函数（radial basis function，RBF）神经网络.与典型三层RBF网络结构相比，该广义RBF网络增加了线性输出加权层.为了克服基于EKF神经网络学习算法由于噪声统计特性未知导致滤波发散或者滤波精度不高的问题，利用EM（expectation maximization）算法对RBF-AR模型噪声协方差矩阵进行估计.同时，通过EKF滤波实时估计RBF-AR模型参数（系统状态），EKF平滑过程得到了更加准确的期望估计.仿真结果显示，该方法用在此变形的RBF-AR模型结构中是有效的，特别在信噪比低的情况下，估计效果比SNPOM（structured nonlinear parameter optimization method）方法好，而且还能估计出噪声方差.F检验显示了两方法估计得到的标准偏差有显著性差异.

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

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.