Blind signal separation from chaotic background
混沌背景下信号的盲分离

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.