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Sign Normalised Hammerstein Spline Adaptive Filtering Algorithm in an Impulsive Noise Environment

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Abstract

In this paper, a sign normalised least mean square algorithm (SNLMS) based on Hammerstein spline adaptive filter (HSAF) is proposed, which is derived by minimising the absolute value of the a posteriori error. The control points, collected in an adaptive lookup table which is interpolated by a local low-order polynomial spline curve and the tap weights of the linear filter are updated by using the direction information of the a posteriori error. The minimization of the absolute value of the a posteriori error reduces the impact of impulsive noises. The new algorithm is called HSAF-SNLMS and can be used to identify the Hammerstein-type nonlinear systems. Furthermore, the convergence performance analysis is carried out by considering the identification of the Hammerstein-type system and the computational complexity of the proposed algorithm is also analyzed. Simulation results in system identification demonstrate the proposed HSAF-SNLMS obtains more robust performance when compared with the existing spline adaptive filter algorithms in impulsive noise environments.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China under Grant 61501119.

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Authors and Affiliations

  1. School of Electronic Engineering, Dongguan University of Techonology, No.1 DaXue Road, Dong’guan, 523808, Guangdong, China

    Chang Liu, Zhi Zhang & Xiao Tang

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  1. Chang Liu
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  2. Zhi Zhang
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  3. Xiao Tang
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Correspondence to Chang Liu.

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Liu, C., Zhang, Z. & Tang, X. Sign Normalised Hammerstein Spline Adaptive Filtering Algorithm in an Impulsive Noise Environment. Neural Process Lett 50, 477–496 (2019). https://doi.org/10.1007/s11063-019-09996-6

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