量化核最小逆双曲正弦自适应滤波算法  

Quantized kernel least inverse hyperbolic sine adaptive filtering algorithm

作　　者：火元莲[1] 脱丽华 齐永锋 张印 Huo Yuan-Lian;Tuo Li-Hua;Qi Yong-Feng;Zhang Yin(College of Physics and Electronic Engineering,Northwest Normal University,Lanzhou 730000,China;College of Computer Science and Engineering,Northwest Normal University,Lanzhou 730000,China)

机构地区：[1]西北师范大学物理与电子工程学院,兰州730000 [2]西北师范大学计算机科学与工程学院,兰州730000

出　　处：《物理学报》2022年第22期355-362,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61561044);甘肃省自然科学基金(批准号:20JR10RA077)资助的课题。

摘　　要：针对非线性问题,本文将核方法和双曲正弦函数的逆相结合,提出了鲁棒的核最小逆双曲正弦算法.然后利用向量量化对输入空间数据进行量化,构建出能够抑制网络规模增长的量化核最小逆双曲正弦算法,降低了原有算法的计算复杂度,给出了量化核最小逆双曲正弦算法的能量守恒关系和收敛条件. Mackey-Glass短时混沌时间序列预测和非线性信道均衡环境的仿真结果表明,本文所提出的核最小逆双曲正弦算法和量化核最小逆双曲正弦算法在收敛速度、鲁棒性和计算复杂度上具有优势.In the last few decades, the kernel method has been successfully used in the field of adaptive filtering to solve nonlinear problems. Mercer kernel is used to map data from input space to reproducing kernel Hilbert space(RKHS) by kernel adaptive filter(KAF). In regenerated kernel Hilbert spaces, the inner product can be easily calculated by computing the so-called kernel trick. The Kernel adaptive filtering algorithm is superior to common adaptive filtering algorithm in solving nonlinear problems and nonlinear channel equalization. For nonlinear problems, a robust kernel least inverse hyperbolic sine(KLIHS) algorithm is proposed by combining the kernel method with the inverse of hyperbolic sine function.The main disadvantage of KAF is that the radial-basis function(RBF) network grows with every new data sample, which increases the computationalcomplexity and requires more momories. The vector quantization(VQ) has been proposed to address this problem and has been successfully applied to the current kernel adaptive filtering algorithm. The main idea of the VQ method is to compress the input space through quantization to curb the network-size growth. In this paper, vector quantization is used to quantify the input spatial data, and a quantized kernel least inverse hyperbolic sine(QKLIHS) algorithm is constructed to restrain the growth of network scale. The energy conservation relation and convergence condition of quantized kernel least inverse hyperbolic sine algorithm are given. The simulation results of Mackey-Glass short-time chaotic time series prediction and nonlinear channel equalization environment show that the proposed kernel least inverse hyperbolic sine algorithm and quantized kernel least inverse hyperbolic sine algorithm have advantages in convergence speed, robustness and computational complexity.

关 键 词：核方法 向量量化 核最小逆双曲正弦算法 短时混沌时间序列预测 

分 类 号：TN713[电子电信—电路与系统]