Duffing振子微弱信号检测盲区消除及检测统计量构造

Blind angle elimination method in weak signal detection with Duffing oscillator and construction of detection statistics

针对Duffing振子进行同频微弱信号检测时存在的检测盲区,提出了一种策动力移相法予以消除.结合微弱信号特性对检测盲区表达式进行分析,得出了策动力与待测信号的"相差"位于检测盲区时的角度范围,通过使策动力相位产生相移量π后实现对同频信号的检测,实验证明了方法的可行性.为了克服定性分析的不足和有效区分振子系统信号检测过程中出现的不同状态,构造了一个基于类Halmiton系统的检测统计量,并设计了基于该统计量的任意频率信号检测方法步骤,方法的核心是以检测统计量出现极大值处所在的连续两个频点作为待测信号的频率范围.在不同检测过程的仿真实验基础上,给出了混沌、间歇混沌和大周期的检测统计量数值范围,进而利用该数值范围作为判据实现了对任意频率信号的检测.实验结果表明,该方法不仅为系统状态提供了定量的判据准则,而且提高了信号检测性能,进一步完善了现有利用Duffing振子进行微弱信号检测的方法.

Aiming at the blind angle in detecting weak signals of the same frequency by Duifing oscillator, a novel metnod of dephasing for the driving signals is proposed to eliminate the blind angle. According to the characteristic of weak signals, expression of blind angle is analyzed, and then the range of blind angle is found out, which corresponds to the amplitude of a new driven signal synthesized from the original driven signals and the unknown one. By making the original driven signal phase shift a degree of lr, detection for the same frequency signal can be realized when the synthesized signal is located in the blind angle region, whose feasibility is proven by an experiment that it remains in chaotic status in the case of blind angle but becomes a great period status after the original driven signal＇s phase is dephased by π. To overcome the drawbacks of qualitative analysis and distinguish effectively different status in signal detection course, a detection statistics based on likelihood-Halmiton system is constructed. On the basis of it, a diagram of detection for any frequency signal is drawn. The key point is to make it as an unknown signal＇s frequency range where there are two adjacent frequency values whose corresponding detection statistics both located in the range of intermittent chaotic status, while one of them is just corresponding to the maximum value of the detection statistics. By simulations of different circumstances, detection statistics for numerical ranges of chaos, intermittent chaos, and great period is summarized. Furthermore, detection for any frequency signal may be realized by use of the numerical range. It is shown that the proposed method could not only provide quantitative judgment for the system status, but improve the signal detection performance. Also, it could be combined well with the traditional oscillator array method or adaptive step intermittent chaotic oscillator method, which further can improve some existing signal detection methods with Duffing oscillator.