【作者】 张海涛；

【导师】 李大字；

【作者基本信息】 北京化工大学 ， 控制理论与控制工程， 2007， 硕士

【摘要】 卡尔曼滤波算法是工业中常用的优化算法之一，广泛应用于去噪、滤波、优化等。由于其优越的数学特性，所以很多的文献中已经将它用于例如前向神经网络以及递归神经网络等一些神经网络的训练。本文首先对各种滤波算法应用于(RBFN)的训练进行仿真研究，找出其优缺点，在此基础上提出了采用无先导卡尔曼滤波算法(Unscented Kalman Filter-UKF)来训练径向基神经网络(RBFN)的新方法。扩展卡尔曼滤波器(EKF)已经被广泛的应用于神经网络的训练。但是本文通过仿真、研究，发现EKF的缺点是当训练集很大的时候，这种算法的计算量将会非常的大而复杂以至于不能完成训练任务，尤其对于RBFN。原因是因为EKF的状态向量包含了所有神经网络参数，这其中包括网络中心点、权值等等内容，运算量非常大。针对这些问题，之后本文尝试运用双重卡尔曼滤波器算法(DEKF)，目的是将作为卡尔曼滤波器状态变量的RBFN参数进行降维，改为由两个并行处理的滤波器进行优化计算，最终结果虽然有一定的改善，但是并没有从根本上解决上述问题。在大量的理论分析以及实际仿真的基础上，我们提出了一种新的用于RBFN训练的算法一无先导卡尔曼滤波器(UKF)算法。针对EKF和DEKF的对函数的一阶近似，该算法中对非线性函数采用二阶近似展开。最重要的一点是UKF不用求取系统的雅克比矩阵，所以大大减小的计算量。仿真结果证明了该方法在时间序列预测、函数逼近以及分类问题上的有效性和运算速度。更多还原

【Abstract】 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.更多还原