Excitation conditions for signed regressor least means squares adaptation

William A. Sethares; Iven M Mareels; Brian Anderson; C. Richard Johnson; Robert R Bitmead

Excitation conditions for signed regressor least means squares adaptation

William A. Sethares, Iven M Mareels, Brian Anderson, C. Richard Johnson, Robert R Bitmead

Research output: Contribution to journal › Article › peer-review

Abstract

The stability of the signed regressor variant of least mean square (LMS) adaptation is found to be heavily dependent on the characteristics of the input sequence. Averaging theory is used to derive a
persistence of excitation condition which guarantees exponential stability of the signed regressor algorithm. Failure to meet this condition (which is not equivalent to persistent excitation for LMS) can result in exponential instability, even with the use of leakage. This new persistence of excitation condition is then interpreted in both deterministic and stochastic settings.

Original language	English
Pages (from-to)	613–624
Journal	IEEE Transactions on Circuits and Systems
Volume	35
Issue number	6
Publication status	Published - Jun 1988

Cite this

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title = "Excitation conditions for signed regressor least means squares adaptation",

abstract = "The stability of the signed regressor variant of least mean square (LMS) adaptation is found to be heavily dependent on the characteristics of the input sequence. Averaging theory is used to derive apersistence of excitation condition which guarantees exponential stability of the signed regressor algorithm. Failure to meet this condition (which is not equivalent to persistent excitation for LMS) can result in exponential instability, even with the use of leakage. This new persistence of excitation condition is then interpreted in both deterministic and stochastic settings.",

author = "Sethares, {William A.} and Mareels, {Iven M} and Brian Anderson and {Richard Johnson}, C. and Bitmead, {Robert R}",

year = "1988",

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T1 - Excitation conditions for signed regressor least means squares adaptation

AU - Sethares, William A.

AU - Mareels, Iven M

AU - Anderson, Brian

AU - Richard Johnson, C.

AU - Bitmead, Robert R

PY - 1988/6

Y1 - 1988/6

N2 - The stability of the signed regressor variant of least mean square (LMS) adaptation is found to be heavily dependent on the characteristics of the input sequence. Averaging theory is used to derive apersistence of excitation condition which guarantees exponential stability of the signed regressor algorithm. Failure to meet this condition (which is not equivalent to persistent excitation for LMS) can result in exponential instability, even with the use of leakage. This new persistence of excitation condition is then interpreted in both deterministic and stochastic settings.

AB - The stability of the signed regressor variant of least mean square (LMS) adaptation is found to be heavily dependent on the characteristics of the input sequence. Averaging theory is used to derive apersistence of excitation condition which guarantees exponential stability of the signed regressor algorithm. Failure to meet this condition (which is not equivalent to persistent excitation for LMS) can result in exponential instability, even with the use of leakage. This new persistence of excitation condition is then interpreted in both deterministic and stochastic settings.

M3 - Article

SN - 0098-4094

VL - 35

SP - 613

EP - 624

JO - IEEE Transactions on Circuits and Systems

JF - IEEE Transactions on Circuits and Systems

IS - 6

ER -

Excitation conditions for signed regressor least means squares adaptation

Abstract

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