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摘要: 核自适应滤波器(Kernel adaptive filter, KAF)是时间序列在线预测的重点研究领域之一, 本文对核自适应滤波器的最新进展及未来研究方向进行了分析和总结. 基于核自适应滤波器的时间序列在线预测方法, 能较好地解决预测、跟踪问题. 本文首先概述了三类核自适应滤波器的基本模型, 包括核最小均方算法、核递归最小二乘算法和核仿射投影算法(Kernel affine projection algorithm, KAPA). 在此基础上, 从核自适应滤波器在线预测的内容和机理入手, 综述基于核自适应滤波器的时间序列在线预测方法. 最后, 本文将介绍这一领域潜在的研究方向和发展趋势, 并展望未来的挑战.Abstract: Kernel adaptive filter (KAF) is one of the significant research fields of time series online prediction. In this paper, the latest development and future research directions of kernel adaptive filter are analyzed and summarized. The time series online prediction algorithms based on kernel adaptive filter can better solve the problem of prediction and tracking. This paper first generalizes the basic models of three types of kernel adaptive filters, including kernel least mean square, kernel recursive least squares and kernel affine projection algorithm (KAPA). On this basis, starting from the content and mechanism of online prediction of kernel adaptive filter, the time online prediction methods for kernel adaptive filter are reviewed. Finally, this paper will introduce the potential research direction and development tendency in this field, and look forward to the challenges ahead.
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图 1 从输入空间到特征空间的非线性映射f(·)
Fig. 1 Nonlinear mapping f(·) from input space to feature space
表 1 不同KAF方法的时间序列在线预测特性对比结果
Table 1 Comparison of online prediction characteristics of time series of different KAF methods
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表 2 每次迭代过程涉及的计算复杂度比较
Table 2 Comparison of computational complexity involved in each iteration
核自适应滤
波器类型在线稀
疏类型计算复杂度 KLMS[19] VQ 更新$ {\alpha} \left( i \right) $ ${\rm O}( { {L^2} } )$ 在线VQ ${\rm O}( { {L} } )$ SF 更新$ {\omega} \left( i \right) $ ${\rm O}( { {L} } )$ 更新$ {e}\left( i \right) $ ${\rm O}( { {L} } )$ KRLS[20] VQ 更新$ {\alpha} \left( i \right) $ ${\rm O}( { {L} } )$ 在线VQ ${\rm O}( { {L} } )$ 更新$ {P}\left( i \right) $ ${\rm O}( { {L^2} } )$ ALD 更新$ {\alpha} \left( i \right) $ ${\rm O}( { {L^2} } )$(${\rm O}( { {L^2} } )$
假如字典改变)更新ALD ${\rm O}( { {L^2} } )$ 更新${P}\left( i \right)$ ${\rm O}( { {L^2} } )$ SW 更新$ {\alpha} \left( i \right) $ ${\rm O}( { {K^2} } )$(${\rm O}( { {K} } )$
假如字典改变)更新${P}\left( i \right)$ ${\rm O}( { {K^2} } )$ 更新${D}\left( i \right)$ ${\rm O}( { {K^2} } )$ FB 更新$ {\alpha} \left( i \right) $ ${\rm O}( { {K^2} } )$(${\rm O}( { {K} } )$
假如字典改变)更新${P}\left( i \right)$ ${\rm O}( { {K^2} } )$ 更新$ {{\hat K}_n}\left( i \right) $ ${\rm O}( { {K^2} } )$ MF 更新$ {\alpha} \left( i \right) $ ${\rm O}( { {L} } )$ 更新$ {e}\left( i \right) $ ${\rm O}( { {L} } )$ 更新${D}\left( i \right)$ ${\rm O}( { {L^2} } )$ CC 更新$ {\alpha} \left( i \right) $ ${\rm O}( { {K^2} } )$(${\rm O}( { {K} } )$
假如字典改变)更新$ {e}\left( i \right) $ ${\rm O}( { {K^2} } )$ 更新${D}\left( i \right)$ ${\rm O}( { {K^2} } )$ KAPA[21] VQ 更新$ {\alpha} \left( i \right) $ ${\rm O}( { {L} } )$ 在线VQ ${\rm O}( { {L} } )$ 更新${P}\left( i \right)$ ${\rm O}( { {L^2} } )$ HC 更新$ {e}\left( i \right) $ ${\rm O}( { {L} } )$ 更新$ {\bf{\zeta }}\left( i \right) $ ${\rm O}( { {L} } )$
下载: 导出CSV
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