Theoretical And Practical Research On Adaptive Combination RBF Filter

Radial basis function neural network has been widely used in many areas because of its advantages such as simple structure, fast learning ability, fast convergence speed, strong approximation performance, no local minimum, easy implementation and strong robustness. Based on the recent research status of radial basis function (RBF) neural network, this dissertation intends to present a in-depth analysis on the basic theory of RBF neural network. In view of the problems existing in the applications of nonlinear signal processing, this dissertation proposes two types of new structure of network based on the convex combination of radial basis function neural network, studies the learning algorithm and improved algorithm, and probes into the application of the nonlinear channel equalization, chaotic time series prediction and nonlinear system identification, etc. The main contents are as follows:This dissertation studies the basic theory of radial basis function neural network systematically and its applications in the field of nonlinear signal processing, and focuses on the applications of the nonlinear filter based on the radial basis function neural network. In view of the impacts on the fixed learning step in the adaptive learning algorithm of RBF network on the convergence speed and steady-state error, that is, big learning step will speed up the convergence rate, but produce more steady-state error. Contrarily, small learning step can reduce the steady-state error, but has to slow down the rate of convergence. Combining the relevant theory of convex combination, we propose a novel nonlinear adaptive filter based on the convex combination of two layers RBF network (CRBF). This nonlinear adaptive filter is composed of the convex combination of two RBF networks with different learning step. Parameters (including the weight coefficients, centers of basis function and spread constants) of each RBF network are updated by SG learning algorithm individually. The advantages of both of the CRBF filter are reserved through the hybrid parameters of the convex combination, so that, fast convergence of the RBF adaptive filter can work with large learning step and low steady-state error of the small one.Based on the novel CRBF nonlinear adaptive filter proposed above, we present an applicable learning algorithm. This adaptive algorithm can automatically adjust the parameters of each of the RBF network and the hybrid parameters of the convex combination that connect the two RBF networks. We have assessed the application of the combinational network in the field of nonlinear channel equalization, nonlinear system identification and chaotic time series prediction and the results of simulation indicate that this type of CRBF network we proposed can not only alleviate the contradiction between convergence speed and steady-state error of the RBF network, but also has better tracking ability.With the detailed and intensive research, this dissertation analyzes the hybrid parameter of the convex combination of two RBF networks and corresponding adaptive algorithm we proposed and presented above. This algorithm uses the principle of gradient descent and adjusts these hybrid parameters adaptively to guarantee that the final combination network possess optimal characteristic with the satisfied. Stability performance is also analyzed in details. Studies show that the convex combination of the RBF network has the best performance on the optimized combination of the RBF network, and has better robustness and tracking ability. More importantly, this combination structure and its adaptive learning algorithm are suitable for online learning.An improved learning algorithm of CRBF network based on minimum index square error was proposed. This algorithm replaces the error cost function of the small step size CRBF network that we proposed above with an index square error cost function with high order statistics, and adjusts the parameters of the network adaptively by using gradient descent rule. This improved learning algorithm is applied to nonlinear adaptive channel equalization, nonlinear system identification and chaotic time series prediction in this dissertation. Simulation results show that the improved learning algorithm outperforms the traditional RBF algorithm with better convergence speed and accuracy.With the improvement on the convex combination of two layers RBF network further, we propose the convex combinations of multiple radial basis function network (MCRBF) nonlinear adaptive filter. This type of filter can be combined by convex combination with any number of independent RBF filter. Each filter has different learning step and can be adjusted to the ideal state by the respective adaptive learning algorithm, so that it can overcome the limitation of the convergence speed and accuracy. In this way, each of the RBF networks of the nonlinear system can follow the tracks of the change of some frequency, and the convex combination of all RBF networks can follow the tracks of various change of any frequency, so it can improve the performance of the whole MCRBF network. In this dissertation, this structure is applied to the nonlinear dynamic system identification, and the detailed research and analysis is made according to different forms of nonlinear system. The results of simulation prove the validity of the MCRBF filter and shows that the overall performance such as convergence speed, steady-state error and tracking ability has been all improved. Moreover, the convex combination of adaptive nonlinear filters that we proposed provides a logical research direction to practical application and can also be used in other nonlinear signal processing field.