利用遞迴 Total Least-Squares 演算法之AR模型適應性建立

Abstract

AR 模型在訊號處理上有廣泛的應用.當輸入訊號包含有高斯白雜訊時, 若 是直接利用RLS 或是 LMS 演算法, 將會得到有偏差的解. 在這篇論文, 我們利用 RTLS 演算法來解決這樣的問題, 並且提出兩種遞迴方法來估計 在 RTLS 演算法中的比重矩陣 D. 若是所求的 AR 模型為窄頻訊號, 則比 重矩陣 D 將近似於單位矩陣. 此時, 對於它的估計則可省略. 模擬的結 果顯示我們所提出的方法明顯地優於傳統的 RLS 演算法. Autogressive(AR) modeling is widely used in signal processing. When theinput data is corrupted by the white Gaussian noise, the direct applicationof the RLS algorithm or LMS algorithm has been shown to yield the biasedsolution. In this thesis, we use the RTLS algorthm to solve the problem, andtwo recursive methods are developed to estimate the weighting matrix D required in the RTLS algorithm. If the AR process is narrow-banded, the weighting matrix can be closed to the identical matrix. In this case, theestimation of D is not required. The simulation results have shown thatthe performance of the proposed method is significantly superior to theconventional RLS algorithm.