STUDY OF GLOBAL CONVERGENCE OF ADAPTIVE IIR FILTER BASED ON PSEUDO LINEAR REGRESSION METHOD
Grant-in-Aid for Scientific Research (C).
|Research Institution||MEIJI UNIVERSITY|
MATSUMOTO Naoki MEIJI UNIVERSITY DEPARTMENT OF ELECTRONICS & COMMUNICATION, SCHOOL OF SCIENCE & TECHNOLOGY PROFESSOR, 理工学部, 教授 (30139464)
|Project Fiscal Year
1997 – 1999
Completed(Fiscal Year 1999)
|Budget Amount *help
¥2,500,000 (Direct Cost : ¥2,500,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1998 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1997 : ¥1,300,000 (Direct Cost : ¥1,300,000)
|Keywords||ADAPTIVE IIR FILTER / EQUATION ERROR / OUTPUT ERROR / LMS / RLS / DECORRELATION / UNIT NORM METHOD / ECHO CANCELER / 適応I I Rフィルタ / 式誤差 / 出力誤差 / 相関除去 / ユニットノルム法 / エコーキャンセラー / 適応IIRフィルター / バイアス / 出力誤差法 / 式誤差法 / 相関除去法 / RLSアルゴリズム / LMSアルゴリズム / 共分散行列 / 適応フィルター / FIRフィルター / ILRフィルター / エコー・キャンセラー / SN比 / 適応フィルタ / エコーキャンセラ- / 相互相関 / FIRフィルタ / 可変ステップアルゴリズム / IIRフィルタ|
The convergence analysis of the pseudo linear regression method (which is equal to output error RLS method with forgetting factor) has been done and its performance has been compared with other adaptive IIR filtering algorithms such as normalized LMS method, equation error RLS method with forgetting factor, unit norm equation error LMS method.
(1) The fastest convergence velocity in the initial phase under high SNR environment is marked by equation error RLS method with forgetting factor. We have explained this result by using a simple statistical model theoretically.
(2) The abrupt change of the characteristics of unknown system causes the slow convergence of equation error RLS method. In case of the output error RLS method with forgetting factor, the convergence velocity is always almost equal even in the initial phase or in the period just after the abrupt change of the characteristics of unknown system.
(3) The slow convergence of the equation error RLS method after the abrupt change
of the characteristics of the unknown system can be improved by reinitializing the covariance matrix of the signal vector. This technique is also valid to output RLS method.
(4) In case of output error RLS method with forgetting factor, the degradation of ERLE can be prevented by using small step size in the update formula for parameter vector. But, in case of equation error method, the degradation of ERLE can not be prevented by step size control.
(5) The parameter vector of the output error RLS method converges to a local optimal solution if unknown system does not satisfy the strictly positive real condition. The theoretical resolution to this hard problem has resulted in fail. However, if we increase the order of the adaptive IIR filter up to three times of that of unknown system, the identification of impulse response is possible within sufficient accuracy under high SNR environment. Hence if we apply the system reduction technique to this result, we can carry out the approximate identification of the unknown systems which do not satisfy strictly positive real condition.
(6) Detection of the abrupt change of SNR and characteristic of unknown system is possible by using NLMS adaptive filter and the author's formula. The development of the adaptive IIR filter which enables those detection is left as the future task. Less
Research Output (21results)