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摘要: 根据混沌序列产生的确定性和非线性机制，基于Volterra级数展式和混沌序列高阶奇异谱特征，提出了一种高阶非线性傅里叶红外(HONFIR)滤波预测模型用于混沌时间序列的自适应预测.其自适应算法采用时域正交算法来自适应地跟踪混沌的运动轨迹，而不是重构混沌系统 的全局或局部运动轨迹.实验研究表明：(1)这种HONFIR自适应滤波器能够有效地预测一些超 混沌序列.(2)预测混沌序列的性能与预测模型的非线性拟合能力有关，但并非非线性程度越 高，预测性能就越好.(3)当HONFIR滤波器对混沌序列的非线性拟合精度高时，其自适应预测 的性能与其输入维数的关系不受Takens嵌入定理的约束.(4)HONFIR自适应滤波器具有一定的 抗噪能力.
Abstract: Based on the Volterra expansion of nonlinear dynamical system functions and the deterministic and nonlinear characterization of the chaotic signals,an adaptive higher-order nonlinear Fourier infrared(HONFIR)filter is proposed to make predic tion of chaotic time series.The time domain orthogonal algorithm is taken to upd ate filter's coefficients.A higher-order nonlinear adaptive filtering scheme is suggested in order to track current chaotic trajectory by using preceding predic tive error for adjustign filter parameters rather than approximating global or l ocal map of chaotic series.Experimental results show that:(1)this adaptive HONFI R filter can be successfully used to predict hyperchaotic time series;(2)the pre diction capacities of the HONFIR filter is related to its nonlinear function,but not determined by the HONFIR filter's degree of nonlinearity;(3)the adaptive pr ediction performance of the HONFIR filter is not confined by the Takens embeddin g dimension;(4)the proposed HONFIR filter can have some anti-noise ability.
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