Robust adaptive filtering algorithms based on (inverse)hyperbolic sine function.

Yong Zhao,Qing Cheng,Qichun Zhang,Bharat Biswal,Sihai Guan

doi:10.1371/journal.pone.0258155

Abstract

Recently, adaptive filtering algorithms were designed using hyperbolic functions, such as hyperbolic cosine and tangent function. However, most of those algorithms have few parameters that need to be set, and the adaptive estimation accuracy and convergence performance can be improved further. More importantly, the hyperbolic sine function has not been discussed. In this paper, a family of adaptive filtering algorithms is proposed using hyperbolic sine function (HSF) and inverse hyperbolic sine function (IHSF) function. Specifically, development of a robust adaptive filtering algorithm based on HSF, and extend the HSF algorithm to another novel adaptive filtering algorithm based on IHSF; then continue to analyze the computational complexity for HSF and IHSF; finally, validation of the analyses and superiority of the proposed algorithm via simulations. The HSF and IHSF algorithms can attain superior steady-state performance and stronger robustness in impulsive interference than several existing algorithms for different system identification scenarios, under Gaussian noise and impulsive interference, demonstrate the superior performance achieved by HSF and IHSF over existing adaptive filtering algorithms with different hyperbolic functions.

Highlights

Adaptive filter (AF) algorithms are frequently employed in linear systems [1,2,3], nonlinear systems [4], and distributed network systems [5] and have been used in many fields, including biomedical engineering [6,7]
logarithmic hyperbolic cosine adaptive filter (LHCAF) was shown to provide better convergence performance compared to the well-known generalized maximum correntropy criterion (GMCC) [27], it may not provide optimal performance as it does not take into account the sparse nature of the system
This paper proposed a family of hyperbolic sine functions, including joint hyperbolic sine function (HSF) and inverse hyperbolic sine function (IHSF), as cost functions

Summary

Introduction

Adaptive filter (AF) algorithms are frequently employed in linear systems [1,2,3], nonlinear systems [4], and distributed network systems [5] and have been used in many fields, including biomedical engineering [6,7]. In an endeavor to achieve lower steady-state misalignment, a generalized hyperbolic secant function as a robust norm and derive the generalized hyperbolic secant adaptive filter was proposed [38] To address both Gaussian and nonGaussian noises with a uniform expression, Liu and colleagues [39] proposed a novel HTCC algorithm by combining nonlinear function and mapping mode. The main contributions of this paper are: (1) development of a robust adaptive filtering algorithm based on hyperbolic sine function (HSF); (2) extend the HSF algorithm to another novel adaptive filtering algorithm based on inverse hyperbolic sine function (IHSF); (3) analyses of the computational complexity for the HSF and IHSF algorithms; (4) validation of the analyses and superiority of the proposed algorithm via simulations. Note: Bold type refers to vectors, [ ]T denotes for the transpose, and [ ]−1 denotes the inverse operation

Hyperbolic sine function

Proposed algorithm based on the hyperbolic sine function

Least hyperbolic sine function

Least inverse hyperbolic sine function

Computational complexity

Simulation results

Conclusions