基于Duffing振子系统的微弱信号检测方法研究

发布时间：2018-12-14 14:27

【摘要】：微弱信号是指幅值比较小的有用信号,通常这类信号容易被强噪声所淹没。传统的微弱信号检测方法主要是基于滤除和抑制噪声,比如窄带滤波、小波分析、取样积分、相关检测等,这些方法检测信噪比门限都比较高且会在一定程度上对有用信号造成损害。因此本论文利用Duffing振子系统对微弱周期信号敏感和对任意零均值噪声免疫的特性,实现低信噪比下对微弱周期信号的有效检测。本论文首先分析了 Duffing振子系统的动力学特性以及噪声对其系统状态的影响,其次分析了系统阈值的判别方法,基于时域及相轨迹方法确定系统阈值并根据Lyapunov指数计算出系统的精确阈值。然后针对目前检测方法所存在的不足进行改进,基于变步长Duffing振子检测系统,通过设定一组能够覆盖待测信号所在频段的仿真步长序列,实现了对低信噪比微弱信号频率的搜索检测;通过相轨迹观察法,实现了对待测信号幅值的检测;通过研究系统在大尺度周期状态时最大Lyapunov指数与待测信号总的策动力幅值的关系,再结合策动力幅值与相位之间的关系,完成了对待测信号初始相位的有效检测。最终完成了对待测信号频率、幅值、相位的参数估计,并利用matlab分别对上述方法进行了仿真实验,验证了方法的有效性及准确性。
[Abstract]:Weak signal is a useful signal with small amplitude, which is usually easily submerged by strong noise. Traditional weak signal detection methods are mainly based on filtering and suppressing noise, such as narrowband filtering, wavelet analysis, sampling integration, correlation detection, etc. These methods have high signal-to-noise ratio (SNR) detection threshold and damage useful signals to some extent. Therefore, the Duffing oscillator system is sensitive to the weak periodic signal and immune to any zero mean noise, so that the weak periodic signal can be detected effectively at low signal-to-noise ratio (SNR). In this paper, firstly, the dynamic characteristics of Duffing oscillator system and the influence of noise on the system state are analyzed. Secondly, the method of judging the threshold value of the system is analyzed. The system threshold is determined based on time domain and phase locus method, and the precise threshold is calculated according to Lyapunov exponent. Based on the variable step size Duffing oscillator detection system, a set of simulation step sequences which can cover the frequency band of the signal to be tested are set. The low signal-to-noise ratio (SNR) weak signal frequency search and detection is realized. The amplitude of the measured signal is detected by the method of phase trajectory observation. By studying the relationship between the maximum Lyapunov exponent of the system and the amplitude of the total driving force of the signal to be measured, and combining the relationship between the amplitude of the excitation force and the phase, the effective detection of the initial phase of the measured signal is accomplished. Finally, the parameter estimation of the frequency, amplitude and phase of the measured signal is completed, and the simulation experiments are carried out using matlab to verify the validity and accuracy of the method.
【学位授予单位】：山东科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.23

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