基于Poincare截面的微弱信号定量检测与幅值参数提取

为解决微弱信号定量检测问题,提出并建立了基于Poincare截面的检测统计量,并以此设计了利用Duffing振子进行微弱信号定量检测及幅值参数提取的有效实现方法。通过分析Duffing振子的Poincare截面特性,发现系统输出关于幅值的分岔特性能够清晰判定系统不同状态,由此对Poincare截面的分布点进行方差统计,构建检测统计量与检测判定区间,实现对微弱信号的定量检测。仿真实验发现，该定量检测方法的噪声鲁棒性优于传统时域特征检测方法,进一步设计了循环检测系统用以提取待测信号幅值参数并实现对未知频率信号的检测，为基于Duffing振子的微弱信号检测提供了定量检测途径与参考。

Weak signal quantitative detection and amplitude parameters extraction based on Poincare section

In order to solve the problem of quantitative detection of weak signals, the detection statistics based on the Poincare section is proposed. An effective quantitative detection method based on the Duffing oscillator is designed, and the amplitude parameters can be extracted with this method. By analyzing the Poincare section characteristics of the Duffing oscillator, it is found that different states of the system can be distinguished by the bifurcation characteristics of the system. Then, the variance statistics of the Poincare section distribution points are determined, the detection statistics and detection determination intervals are formulated to realize the quantitative detection. The simulation results show that the noise robustness of the quantitative detection method is better than that of the traditional time-domain feature detection method. Furthermore, a cyclic detection system is designed to extract the amplitude parameters and detect the unknown frequency signals. The results provide a quantitative detection approach and reference for weak signals detection based on the Duffing oscillator.