Sparse leaky-LMS algorithm for system identification and its convergence analysis.

*(English)*Zbl 1337.93093Summary: In this paper, a novel adaptive filter for sparse systems is proposed. The proposed algorithm incorporates a log-sum penalty into the cost function of the standard leaky Least Mean Square (LMS) algorithm, which results in a shrinkage in the update equation. This shrinkage, in turn, enhances the performance of the adaptive filter, especially, when the majority of unknown system coefficients are zero. Convergence analysis of the proposed algorithm is presented, and a stability criterion for the algorithm is derived. This algorithm is given a name of Zero-Attracting leaky-LMS (ZA-LLMS) algorithm. The performance of the proposed ZA-LLMS algorithm is compared to those of the standard leaky-LMS and ZA-LMS algorithms in sparse system identification settings, and it shows superior performance compared to the aforementioned algorithms.

##### MSC:

93E11 | Filtering in stochastic control theory |

93C40 | Adaptive control/observation systems |

93E24 | Least squares and related methods for stochastic control systems |

93E10 | Estimation and detection in stochastic control theory |

93E12 | Identification in stochastic control theory |

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\textit{M. S. Salman}, Int. J. Adapt. Control Signal Process. 28, No. 10, 1065--1072 (2014; Zbl 1337.93093)

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