應用 Steiglitz-McBride 方法的適應性 IIR 陷波器

Abstract

在此文中我們提出一種適應性陷波器 (Adaptive Notch Filter,"ANF")， 以估測被雜訊干擾之正弦波的頻率。此 ANF 的結構是以 ALE (Adaptive Line Enhancement) 的架構配合 Steiglitz-McBride Method (SMM) ，並 使用限定極零點鏡影對稱的陷波器為模型所得到的。當 ALE 架構中延遲 時間 'delta'=1 時，此陷波器在 'rho'=1 時與 IFA (Iterative Filtering Algorithm) 相同，在'rho' < 1 則與 RGLS (Recursive Generalized Least Square) 相等。若選擇恰當 'delta' 值，此陷波器 對有色雜訊 (Color Noise) 干擾的正弦波訊號頻率之估測會更準確。此 陷波器若以離線 (Off-Line) 執行時，在白雜訊干擾下，可以保證一定收 斂；但若是以線上 (On-Line) 執行時，我們提出一充分條件以保證此方 法收斂。此陷波器的追蹤特性可經由分析而得到如同 RML (Recursive Maximum Likelihood) 方法的優良結果。由許多模擬結果顯示此陷波器收 斂特性與 RML 的結果類似，但解析度 (Resolution) 遠較 RML 高，而且 在恰當初值選擇下，此陷波器不需要穩定度的檢查 (Stability Monitoring)。由於此陷波器實現所需計算量小，收斂速度快，偏移量 (Bias) 小，解析能力高，追蹤能力亦強，而且可在有色雜訊的環境使用 ，所以非常適合實際上的應用。 In this thesis, we present a new adaptive notch filter (ANF) toestimate frequencies of multiple narrow-band signals or sine waves in an additive broad-band noise.The new ANF model is derivedby combining the adaptive line enhancement (ALE) structurewith the Steiglitz-McBride Method (SMM) with constrained poles and zeros.When the decorrelation delay parameter 'delta'=1, the new ANFis shown to be equivalent to iterative filtering algorithm (IFA) model for'rho'=1, and is equivalent to recursive generalized least square (RGLS) model for 'rho' < 1.If the observed measurement data is corrupted by color noise,the new ANF still can provide accurate frequency estimation if we choose appropriate value of 'delta'.When the new ANF is executed off-line, the algorithmwill converge if the noise is white. When the new ANF isexecuted on-line, we provide a sufficient conditionfor the new ANF. When the condition is met, the on-linealgorithm will converge.The tracking property of the new ANF is analyzed for white noisecase and is shown to have the same tracking performance as that of RML (Recursive Maximum Likelihood).Extensive simulations show that the convergence properties of the proposed ANF are comparable to those of RML, and the new ANF has better frequency resolution. The proposed ANF does not needthe stability monitoring if the initial guess is stable.The new ANF is computationally simple and hasfast convergent speed, and the bias of convergent point is small.It also has good frequency resolution and high frequency tracking capability. Therefore, the new ANF is suitablefor practical applications.