Necessary and sufficient conditions for stability of LMS [Elektronisk resurs] / L. Guo, L. Ljung, G.J. Wang
Guo, Lei (författare)
Ljung, Lennart, 1946- (författare)
Wang, Guan-Jun (författare)
- Linköping : Linköping University Electronic Press, 1995
- Engelska 25 s.
Serie: LiTH-ISY-R, 1400-3902 ; 1805
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- Guo and Ljung (1995) established some general results on exponential stability of random linear equations, which can be applied directly to the performance analysis of a wide class of adaptive algorithms, including the basic LMS ones, without requiring stationarity, independency, and boundedness assumptions of the system signals. The current paper attempts to give a complete characterization of the exponential stability of the LMS algorithms by providing a necessary and sufficient condition for such a stability in the case of possibly unbounded, nonstationary, and non-φ-mixing signals. The results of this paper can be applied to a very large class of signals, including those generated from, e.g., a Gaussian process via a time-varying linear filter. As an application, several novel and extended results on convergence and the tracking performance of LMS are derived under various assumptions. Neither stationarity nor Markov-chain assumptions are necessarily required in the paper.
Indexterm och SAB-rubrik
- Least mean squares algorithm
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