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Adaptive filtering using Lyapunov theory and artificial intelligent techniques

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Seng, KP (2001) Adaptive filtering using Lyapunov theory and artificial intelligent techniques. PhD thesis, University of Tasmania.

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Abstract

Adaptive filtering has gained popularity in numerous applications to help cope with
time-variations of system parameters, and to compensate for the lack of a priori
knowledge of statistical properties of the input data. Therefore, it is an area of research
that has important implications for many problems in signal processing, control and
estimation, communication and others. Over the last several decades, a wide range of
filter structures and algorithms has been developed. Finite Impulsive Response (FIR) and
Infinite Impulse Response (UR) transversal filters are two well-established linear models
for adaptive filtering. However, there are several circumstances that the performances of
these filters are unsatisfactory. Nonlinear polynomial filtering had been first considered
by some researchers. More recently, artificial intelligent techniques such as neural
networks and fuzzy logic have undergone rapid development and become recognized as
powerful nonlinear approximation methods. Hence various nonlinear adaptive filtering
techniques using multi-layer perceptron (MLP), radial basis function (RBF) and fuzzy
logic have been developed.
Adaptive filtering algorithm is another important topic for adaptive filtering. There are
two well-studied algorithms for adaptive filtering: recursive least squares (RLS) and
least mean square (LMS) algorithms. LMS algorithm attempts to minimize the mean
square of the error signal by employing a stochastic gradient technique. It is strongly
dependent on the input signal spectral characteristics and its convergence depends on the
eigen-value spread of the autocorrelation matrix. In contrast, several advantages of RLS
over LMS in terms of tracking behavior and fast convergence are well known. It is
independent of input spectral characteristics but it is of high computational complexity.
Furthermore, it exhibits unstable performance. Methods of avoiding instability have
been proposed in the literature but the stability problems of adaptive filters have not
been solved if there are some bounded input disturbances.

Item Type: Thesis (PhD)
Keywords: Lyapunov stability, Adaptive filters, Fuzzy algorithms, Adaptive control systems
Copyright Holders: The Author
Copyright Information:

Copyright 2001 the author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).

Additional Information:

For consultation only. No loan or photocopying permitted until 31 November 2003. Thesis (Ph.D.)--University of Tasmania, 2001. Includes bibliographical references

Date Deposited: 03 Feb 2015 03:20
Last Modified: 17 Oct 2016 22:26
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