用Householder變換的遞推AR模型化與譜估計算法
A RECURSIVE ALGORITHM FOR AR MODELING AND SPECTRAL ESTIMATION USING HOUSEHOLDER TRANSFORM
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摘要: Housecholder變換用于上三角化是基于線性預(yù)測誤差方程的數(shù)據(jù)陣?？梢宰C明,由上三角陣的主對角元素便可得到各階AR模型的殘差平方和。因此用逐列處理的方法可以構(gòu)成 AR 模型化與譜估計的遞推算法。在大多數(shù)情況下,本文的算法不僅給出與協(xié)方差算法或修正協(xié)方差算法相同的計算結(jié)果;而且當計算中存在嚴重的數(shù)值病態(tài)問題時,協(xié)方差法和修正協(xié)方差法無法獲得好的AR譜估計,而本文的算法則仍然可以獲得好的估計。文中給出了典型的計算例子。
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關(guān)鍵詞:
- AR譜估計; Householder變換; AR參數(shù); 遞推算法
Abstract: Householder transform is used to triangularize the data matrix which is based on the linear prediction error equation. It is proved that the sum of squared residuals for each AR order can be obtained by the main diagonal elements of upper triangular matrix, so the column by column procedure can be used to develop a recursive algorithm for AR modeling and spectral estimation. In the most cases, the presented algorithm yield the same results as the covariance method or modified covariance method does. But in some special cases where the numericall ill-conditioned problems are so serious that the covariance method and inodified covariance method fail to estimate AR spectrum, the presented algorithm still tends to keep good performance. The typical computational results are given finally. -
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