Application of Wilcoxon Norm for increased Outlier Insensitivity in Function Approximation Problems

Abstract

In system theory, characterization and identification are fundamental problems. When the plant behavior is completely unknown, it may be characterized using certain model and then, its identification may be carried out with some artificial neural networks(ANN) (like multilayer perceptron(MLP) or functional link artificial neural network(FLANN) ) or Radial Basis Functions(RBF) using some learning rules such as the back propagation (BP) algorithm. They offer flexibility, adaptability and versatility, for the use of a variety of approaches to meet a specific goal, depending upon the circumstances and the requirements of the design specifications. The first aim of the present thesis is to provide a framework for the systematic design of adaptation laws for nonlinear system identification and channel equalization. While constructing an artificial neural network or a radial basis function neural network, the designer is often faced with the problem of choosing a network of the right size for the task. Using a smaller neural network decreases the cost of computation and increases generalization ability. However, a network which is too small may never solve the problem, while a larger network might be able to. Transmission bandwidth being one of the most precious resources in digital communication, Communication channels are usually modeled as band-limited linear finite impulse response (FIR) filters with low pass frequency response.