基于互相关和李雅普诺夫指数的微弱正弦信号混沌检测

微弱信号的幅值通常很小，且常被噪声淹没，难以检测。文中提出基于互相关和李雅普诺夫指数的微弱正弦信号混沌检测方法。该方法利用互相关方法对微弱正弦信号进行初步去噪，再利用混沌检测方法提取有效信号，以充分发挥互相关及混沌检测在噪声抑制及信号提取方面的优势;将最大李雅普诺夫指数作为判断混沌系统相变的量化依据，自动识别混沌系统的临界状态，从而准确给出用于确定微弱正弦信号幅值的策动力临界阈值。仿真实例分析表明，该方法能有效地检测出深埋于强噪声中的微弱正弦信号，且其检测精度较单独的互相关方法和混沌检测方法更优。

Chaotic Detection of Weak Sine Signals Based on Cross-correlation and Lyapunov Exponent

A weak signal is basically difficult to detect because its magnitude is small and it is often submerged in noised. A chaotic detection method for weak sine signals based on the cross-correlation and the Lyapunov exponent is given. Firstly, the cross-correlation method is applied to preliminarily remove noises, and then the chaotic detection method can be used to extract the weak sine signal. The proposed method adequately exerts the noise reduction ability of the cross-correlation method and the signal extraction ability of the chaotic detection method. Moreover, the proposed method uses Lyapunov exponent as the judgment criterion of chaotic dynamics. It can automatically recognize the critical state between the chaotic motion and the periodic motion and give the exact threshold value which is used to calculate the weak sine signal. Simulation results show that the proposed method can detect weak sine signals in strong noise, and the detection precision is superior to that of the cross-correlation method and the chaotic detection method.