Lyapunov指数算法在微弱信号检测中的应用  

Application of Lyapunov exponent algorithm in the weak signal detection

作　　者：王冀超[1] 杨正华[1] 岳亮[1] 廖文鹏[1] 

机构地区：[1]长安大学地质工程与测绘学院,西安710054

出　　处：《电子测量技术》2017年第8期164-168,188,共6页Electronic Measurement Technology

摘　　要：基于MATLAB/Simulink仿真软件,分析了Holmes-Duffing系统检测弱正弦信号的原理和仿真实验步骤。通过仿真结果表明,直接从相平面图中肉眼观察混沌临界状态的阈值容易存在较大的人为误差。针对这个问题,提出了利用Lyapunov指数算法来定量地分析系统的动力学特征,并进一步研究了最大Lyapunov指数与系统状态之间的关系。对临界区域进一步取值发现其LE指数在零点振荡跳跃说明了该混沌系统正处于间歇临界态。最后通过对信噪比为-40dB的微弱信号进行检测来说明,采用Lyapunov指数算法能够更直观地判断微弱信号的存在,证明其检测方法的可行性。Based on the Matlab/Simulink simulation software, the principle of the weak sine signal detection and the simulation experiment steps are analyzed in the Holmes-Dulling system. The simulation results show that there is a large human error in the threshold value of the chaotic state directly from the phase diagram. Aiming at this problem, the Lyapunov exponent algorithm is proposed to quantitatively analyze the dynamic characteristics of the system and research the relationship between the maximal Lyapunov exponent and the system state. The further analysis of the critical region discovers that the LE exponent in the zero oscillation shows that the chaotic system is in the intermittent criticality. Finally, the weak signal with signal to noise ratio of --40 dB is tested to show that the Lyapunov exponent algorithm can judge the existence of weak signals more accurately, which proves the feasibility of the detection method.

关 键 词：微弱信号检测 Holmes-Duffing混沌振子 相平面图 临界阈值 LYAPUNOV指数 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术] TN911.23[自动化与计算机技术—计算机科学与技术]