基于扩展卡尔曼滤波器的RBF神经网络学习算法

Learning Algorithm of RBF Neural Networks Based on Extended Kalman filter

径向基函数(RBF)神经网络可广泛应用于解决信号处理与模式识别问题,目前存在一些学习算法用来确定RBF中心节点和训练网络,对于确定RBF中心节点向量值和网络权重值可以看作同一系统问题,因此该文提出把扩展卡尔曼滤波器(EKF)用于多输入多输出的径向基函数(RBF)神经网络作为其学习算法,当确定神经网络中网络节点的个数后,EKF可以同时确定中心节点向量值和网络权重矩阵,为提高收敛速度提出带有次优渐消因子的扩展卡尔曼滤波器[1](SFEKF)用于RBF神经网络学习算法,仿真结果说明了在学习过程中应用EKF比常规RBF神经网络有更好的效果,学习速度比梯度下降法明显加快,减少了计算负担。

Radial basis function （RBF） neural networks provide attractive possibilities for solving signal processing and pattern classification problems. Several algorithms have been proposed for choosing the RBF prototypes and training the network. The selection of the RBF prototypes and the network weights can be viewed as a system identification problem. As such, this paper proposes the use of the extended Kalman filter （EKF） for learning procedure, after the user chooses how many prototypes to include in the network, the Kalman filter simultaneously solves for the prototype vectors and the weight matrix. In order to elevate speed of convergence, this paper proposes the use of the suboptimal fading extended Kalman filter （SFEKF） for learning procedure. The experimental results show that the use of he extended Kalman filter results in better learning than conventional RBF networks and faster learning than gradient descent, reducing computational burden.