Almost-sure convergence of the continuous-time LMS algorithm
The authors consider the stability properties of the conventional continuous-time least mean square algorithm. The algorithm for the case of stationary ergodic inputs is investigated and a necessary and sufficient condition for exponential almost-sure convergence is presented. This condition is show...
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| Published in | IEEE transactions on signal processing Vol. 40; no. 2; pp. 395 - 401 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.02.1992
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1053-587X |
| DOI | 10.1109/78.124949 |
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| Abstract | The authors consider the stability properties of the conventional continuous-time least mean square algorithm. The algorithm for the case of stationary ergodic inputs is investigated and a necessary and sufficient condition for exponential almost-sure convergence is presented. This condition is shown to be less restrictive than the well-known persistency of excitation condition. Also, the authors point out and clarify an apparently common error regarding the connections between persistency of excitation and positive definite autocorrelation in stationary ergodic vector waveforms.< > |
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| AbstractList | The authors consider the stability properties of the conventional continuous-time least mean square algorithm. The algorithm for the case of stationary ergodic inputs is investigated and a necessary and sufficient condition for exponential almost-sure convergence is presented. This condition is shown to be less restrictive than the well-known persistency of excitation condition. Also, the authors point out and clarify an apparently common error regarding the connections between persistency of excitation and positive definite autocorrelation in stationary ergodic vector waveforms The authors consider the stability properties of the conventional continuous-time least mean square algorithm. The algorithm for the case of stationary ergodic inputs is investigated and a necessary and sufficient condition for exponential almost-sure convergence is presented. This condition is shown to be less restrictive than the well-known persistency of excitation condition. Also, the authors point out and clarify an apparently common error regarding the connections between persistency of excitation and positive definite autocorrelation in stationary ergodic vector waveforms.< > |
| Author | Kozin, F. Voltz, P.J. |
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| Cites_doi | 10.1109/29.17546 10.1109/9.16424 10.1109/PROC.1976.10378 10.1109/TAC.1977.1101401 10.1109/TAC.1980.1102427 |
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| References | doob (ref7) 1953 ref4 sastry (ref1) 1989 ref6 sondhi (ref3) 1976; 64 ref5 ref2 |
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| Snippet | The authors consider the stability properties of the conventional continuous-time least mean square algorithm. The algorithm for the case of stationary ergodic... |
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| StartPage | 395 |
| SubjectTerms | Adaptive arrays Adaptive control Autocorrelation Convergence Least squares approximation Stability Sufficient conditions System identification Vectors |
| Title | Almost-sure convergence of the continuous-time LMS algorithm |
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