Adaptive recursive algorithm with logarithmic transformation for nonlinear system identification in α-stable noise

Although the least mean pth power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filters outperform the conventional least mean square (LMS) algorithm in the presence of α-stable noise, they still exhibit slow convergence and high steady-state kernel error in nonlinear system identi...

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Vydáno v:Digital signal processing Ročník 46; s. 120 - 132
Hlavní autoři: Zhao, Haiquan, Lu, Lu, He, Zhengyou, Chen, Badong
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.11.2015
Témata:
Logarithmic transformation
Nonlinear system identification
Volterra filter
α-stable noise
α-stable noise
Volterra filter
Logarithmic transformation
Nonlinear system identification
ISSN:1051-2004, 1095-4333
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Popis
Shrnutí:Although the least mean pth power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filters outperform the conventional least mean square (LMS) algorithm in the presence of α-stable noise, they still exhibit slow convergence and high steady-state kernel error in nonlinear system identification. To overcome these limitations, an enhanced recursive least mean pth power algorithm with logarithmic transformation (RLogLMP) is proposed in this paper. The proposed algorithm is adjusted to minimize the new cost function with the p-norm logarithmic transformation of the error signal. The logarithmic transformation, which can diminish the significance of outliers under α-stable noise environment, increases the robustness of the proposed algorithm and reduces the steady-state kernel error. Moreover, the proposed method improves the convergence rate by the enhanced recursive scheme. Finally, simulation results demonstrate that the proposed algorithm is superior to the LMP, NLMP, normalized least mean absolute deviation (NLMAD), recursive least squares (RLS) and nonlinear iteratively reweighted least squares (NIRLS) algorithms in terms of convergence rate and steady-state kernel error. •An enhanced recursive least mean pth power algorithm with logarithmic transformation is proposed.•The new cost function with the p-norm logarithmic transformation of the error signal is presented.•The convexity of the proposed cost function is demonstrated.•The convergence performance of the proposed RLogLMP algorithm is analyzed.
ISSN:1051-2004
1095-4333
DOI:10.1016/j.dsp.2015.08.004