Research On Training Of Radial Basis Function Network Based On Kalman Filter Algorithm

Kalman Filter has been widely used in modern industry such as noise-reducing, filtering, optimizing, and so on. It has been involved in training feedforward neural networks and recurrent neural networks because of its excellent mathematic characteristic in many researches. In this thesis, RBFN was trained using several kinds of Kalman filter, their disadvantages and merits were studied, and eventually, a method of applying unscented Kalman Filter(UKF) for training of RBF neural network was proposed .Extended Kalman Filter has been successfully used for training neural networks. In the study, simulation results show that EKF can't complete the training mission when the training set is too large, especially for RBFN. The reason is thatthe state vector of EKF for training RBF neural network including all the parameters of the network, such as kernel points, weights of thelayers and so on, so the calculational complexity is significantly large. Aim at the point, the dual Extended Kalman filter (DEKF) was tested for reducing the dimensions of the EKF's state vector. Though it improves calculational complexity at a certain extent, DEKF can't change essential disadvantage.A new method for training RBFN named "Unscented Kalman Filter" (UKF) through a mass of academic analysis based on the optimization was proposed instead. Different from EKF and DEKF which execute first order approximation, UKF uses second order approximation to extend nonlinear function. And the most important is: UKF doesn't need to calculate system Jacobian matrix so the calculational complexity of training process can be reduced signaflcantly. Simulation results show its validity and speediness in function approximation, chaotic time series prediction and classification problems.