摘要
近幾年來，可適性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，遞迴最小平方和(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。然而在某些應用上，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。通常非線性濾波器本身的結構是很複雜的，這會導致運算量過大而降低其實用性。 在本論文中，我們將快速牛頓演算法以及快速RLS Volterra演算法加以整合，發展出快速Volterra牛頓適應演算法(FVNTF)。當輸入訊號為M階的AR隨機程序時，我們可將估測器的長度設定為M，其中M遠小於系統模式長度L，藉此可大幅度降低快速RLS Volterra的運算量，同時，FVNTF演算法能展現出近乎RLS Volterra演算法的快速收斂特性。
並列摘要
Adaptive filters have 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 is proportional to the square of the number of coefficients. Fast RLS and fast Newton transversal filtering algorithms are modified versions 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 very 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 Volterra Newton transversal filter (FVNTF) by integrating fast Newton transversal filter and fast RLS Volterra algorithms. Our new algorithm has a performance that is close to the RLS Volterra while requires a much lower complexity than the fast RLS Volterra when the input signal is that of an AR process with order M which is much smaller than system order L。
參考文獻
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