一種新的快速遞迴最小平方誤差的Volterra 適應演算法

A Fast Newton Transversal Filter Second-Order Volterra Filtering Algorithm

張勝傑(Sheng-Chieh Chang)

指導教授 ： 李仲溪

元智大學/工程學院/電機與資訊工程研究所/碩士(1998年)

摘要

摘 要
近幾年來，可適應濾波器已被廣泛的應用於通訊及控制領域。在各種適應演算法中，遞迴最小平方誤差演算法(RLS)能提供很好的效能，只是其使用到的運算量與濾波器係數長度的平方成正比，因此當適應濾波器本身的係數長度過長時，這種演算法則不實際。快速RLS以及快速牛頓演算法則都是RLS的改良。線性濾波器具有簡單、易實現的特性。但在某些應用時，線性濾波器所能提供的效能不如非線性濾波器來的良好，我們因此會考慮使用非線性濾波器。然而，非線性濾波器本身的結構通常是很複雜的，這會導致運算量過大而降低其實用性。在本篇論文中，我們將快速牛頓演算法應用到二階的Volterra濾波器，當輸入信號為自相關隨機程序時，我們所發展的演算法具有接近RLS的效能表現，而其運算量則遠低於RLS演算法。

關鍵字

可適應濾波器 ； 適應演算法 ； 快速牛頓演算法 ； 遞迴最小平方誤差 ； 快速RLS

並列摘要

Abstract
Adaptive filtering has been widely employed in the fields of communications and automatic control. Among various types of adaptive filtering algorithms, the performance of recursive least squares (RLS) is quite satisfactory. However, the RLS has a computational complexity that increases as the square of the number of coefficients. Fast RLS and fast Newton transversal filter algorithms are modified formulations of the RLS algorithm in such a way that the computational complexity increases linearly with the number of taps. Due to its simplicity, linear filter is popular in applications. However, the performance of linear filter is just not acceptable in some applications where nonlinearity of the system is not negligible. Therefore, nonlinear filter is a natural alternative. A major concern with nonlinear filtering is the complexity. In this thesis, we develop a fast Newton type algorithm equipped with a second-order Volterra filter. Our new algorithm has a performance that is close to the RLS algorithm while requires a much lower complexity than the RLS when the input signal is that of an AR process.

並列關鍵字

Adaptive Filter ； Adaptive Filtering Algorithms ； Fast Newton Transversal Filter ； Recursive Least Squares ； Fast RLS

參考文獻

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