混沌背景下信号的盲分离

混沌信号与确定性小信号叠加生成的混合信号是一更高维的混沌信号,因而不能用一般的混沌信号噪声抑制的方法进行分离.提出了一种这类信号盲分离的方法.在重构未知的混沌信号的动力方程时,充分利用混沌吸引子的几何特性,并且限定动力映射为原混沌吸引子所在流形的内部映射,从而保证了重构的动力系统方程对应于原混沌信号,而不是同样具有混沌特性的混合信号.然后利用重构的动力方程,借用混沌信号中的噪声抑制思想,估计出原混沌信号对应的轨道,实现信号分离.通过对Lorenz系统中谐波信号、Henon映象中自回归过程,以及脑电信号中谐波信号进行提取的数值实验,验证了信号盲分离方法的有效性和可行性. 关键词： 混沌 非线性 信号处理 盲分离

Blind signal separation from chaotic background

To separate a weak deterministic signal from a chaotic background of which the dynamic mechanism is unknown is a different problem from the noise reduction for a chaotic signal since the mixed signal is also a chaotic signal with higher dimension than the original chaotic system. This paper presents a blind separation method in which the dynamical equations of the original chaotic signal are reconstructed based on the knowledge of the geometric characteristic and the dynamical information of the chaotic attractor and the restriction that the map of the equations is limited in the estimated manifold of the original chaotic attractor. Thus, the reconstructed dynamical equations are guaranteed to be original chaotic system instead of mixed chaotic one. Having reconstructed the original chaotic equations, the trajectory of the corresponding chaotic signal can be estimated and thus the weak deterministic signal can be separated using the principles of noise reduction for a chaotic signal. Some simulations such as a harmonic extraction from Lorenz signal, an autoregressive signal extraction from Henon map and a harmonic extraction from electroencephalograph signal verified the effectiveness and adaptability of the proposed method.