基于Duffing混沌振子的微弱信号检测研究

摘要

Traditional weak signal detection methods have poor performance when detecting weak signals, while Duffing oscillator shows good detection effect since it is sensitive to iinitial condition and has good resistance to noise. The basic form and dynamical evolution process of Duffing equation are analyzed, the operation principle of weak signal detection based on phase plane changes is introduced, a novel method for accurately determining the phase change threshold is proposed, and the influence of noise on the threshold is discussed. MATLAB software is used for simulation, the result of which shows that weak signals can be detected with a signal-to-noise ratio of-130 dB.%传统的微弱信号检测方法在检测信噪比很低的信号时效果很差,而Duffing振子混沌系统由于具备对初值敏感、对噪声具有较好的抵抗力等优点,因此在检测微弱信号能够表现出良好的检测效果。分析了Duffing方程的基本形式和动力学演化过程,阐述了基于相平面变化进行微弱信号检测的工作原理。提出了一种准确确定相变阈值的方法,讨论了高斯白噪声对阈值的影响。按照提出的检测步骤,应用MATLAB软件进行仿真,仿真结果表明可以检测出的微弱信号的信噪比能达到-130 dB。