A Robust Student’s <i>t</i>-Based Kernel Adaptive Filter
Haojie Wang, Xifeng Li, Dongjie Bi, Xuan Xie, Yongle Xie
Abstract
In this brief, a kernel adaptive filter based on the Student’s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${t}$ </tex-math></inline-formula> distribution in the reproducing kernel Hilbert space (RKHS) is presented, which is distinct from the traditional kernel adaptive filtering algorithms as follows: first, a Student’s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${t}$ </tex-math></inline-formula> reproducing kernel function is proposed to fight against the abrupt noise together with Gaussian noise depicted by the impulsive-Gaussian mixed noise model; and second, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Strengthened Surprise Criterion</i> (SSC) is devised to reduce the size of the neural networks, which is utilized to implement the proposed Student’s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${t}$ </tex-math></inline-formula> -based kernel filter. The proposed algorithms are compared with the widely used KLMS and recently proposed KRLS-type filters in terms of the accuracy error under both Gaussian and abrupt noise. Experimental results show that the proposed Student’s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${t}$ </tex-math></inline-formula> -based kernel adaptive filter can improve the estimation accuracy at least by 20% while having more compact size of neural networks compared with the existed kernel adaptive algorithms.