Two variants of the IIR spline adaptive filter for combating impulsive noise

Chang Liu,Xueliang Liu,Xiao Tang,Chao Peng

doi:10.1186/s13634-019-0605-9

Chang Liu, Xueliang Liu + Show 2 more

Open Access

https://doi.org/10.1186/s13634-019-0605-9

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Abstract

It has been pointed out that the nonlinear spline adaptive filter (SAF) is appealing for modeling nonlinear systems with good performance and low computational burden. This paper proposes a normalized least M-estimate adaptive filtering algorithm based on infinite impulse respomse (IIR) spline adaptive filter (IIR-SAF-NLMM). By using a robust M-estimator as the cost function, the IIR-SAF-NLMM algorithm obtains robustness against non-Gaussian impulsive noise. In order to further improve the convergence rate, the set-membership framework is incorporated into the IIR-SAF-NLMM, leading to a new set-membership IIR-SAF-NLMM algorithm (IIR-SAF-SMNLMM). The proposed IIR-SAF-SMNLMM inherits the benefits of the set-membership framework and least-M estimate scheme and acquires the faster convergence rate and effective suppression of impulsive noise on the filter weight and control point adaptation. In addition, the computational burdens and convergence properties of the proposed algorithms are analyzed. Simulation results in the identification of the IIR-SAF nonlinear model show that the proposed algorithms offer the effectiveness in the absence of non-Gaussian impulsive noise and robustness in non-Gaussian impulsive noise environments.

Highlights

Due to their concise design and low complexity, the adaptive linear filters have gained wide attention in system modeling and identification [1, 2]
In order to model the nonlinearity, several adaptive nonlinear structures have been presented such as truncated Volterra adaptive filters (VAF) [3], neural networks (NNs) [4], block-oriented architecture [5], and spline adaptive filters (SAF) [6,7,8,9]
It can be clearly seen that the larger value of θ leads to the faster convergence rate, and the proposed infinite impulse response (IIR)-SAF-SMNLMM gets nearly similar steady-state mean square error (MSE) for different values of θ

Summary

Introduction

Due to their concise design and low complexity, the adaptive linear filters have gained wide attention in system modeling and identification [1, 2]. Combining the block-oriented architecture with the spline function, several novel adaptive nonlinear spline adaptive filters (SAFs) have been introduced such as Wiener spline filter, Hammerstein spline filter, cascade spline filter and IIR spline adaptive filter (IIRSAF) These spline adaptive models can be implemented by different connections of the spline function and linear time-invariant (LTI) model. In each iteration, only a portion of the control points is tuned depending on the order of the spline function and the nonlinear shape is slightly changed This local behavior of the spline function results in the considerable saving in the computation complexity. To further improve the convergence performance of the IIR-SAFNLMM, we incorporate the set-membership framework into the IIR-SAF-NLMM and propose a set-membership IIR-SAF-NLMM (IIR-SAF-SMNLMM) algorithm It is derived by minimizing a new M-estimate-based cost function associated with a robust set-membership error bound.

Proposed IIR-SAF-NLMM and IIR-SAF-SMNLMM algorithms

IIR-SAF-SMNLMM algorithm

Computational complexity

Results and discussion

Conclusions