混沌振子状态检测统计量模型及其在微弱信号检测中的应用研究

Weak signal detection from strong noise is one important problem in engineering area. Traditional method based on linear and certain system could only realize detection in limited range of signal to noise ratio (SNR), while Duffing oscillator as one typical representative of chaotic detection technology could reach detection in very low signal to noise ratio, which draws high attention more and more. Principle of Duffing oscillator is to finish detection by system status’ viriation from chaos to great period or from chaos to intermittent chaos. However, most of methods existed now only realize signal detection by qualitative analysis for phase plane diagram or time domain diagram, which will bring some subjectivity and have low reliability and accuracy. Our subject is just to overcome these drawbacks. On basis of time-frenquency analysis and other analysis ways for system status output sequence, mathematical statistics law of different status will be studied, then mathematical model of status characteristic quantity will be built, which should consider status vector (status sequence) , sequence length, amplitude of driven signal, frenquency and other factors. Thus, detection statistic constructed by status characteristic quantity could provide quantitative judgement for different status, which would improve detection efficiency and scientificy. Further more, combining detection statistic with oscillator array or frequency control unit in driven signal, could realize weak signal detection for random frenqucncy, whose whole method flow of this process will be construced in the project. The research can polish signal detection theory of Duffing oscillator and its algorithm realization, which has some reference values for weak signal detection area.

强噪声背景下的微弱信号检测是工程领域的一类重要问题。传统基于线性、确定性系统的方法所能检测到的信噪比范围有限，以Duffing振子为代表的混沌检测技术能达到很低的信噪比，因而备受关注。其原理为通过系统状态从混沌态向大周期态，或混沌态到间歇混沌态的变化来实现检测，但目前方法多停留在定性分析相图或时域图的层面，具有一定的主观性，可靠性和精确性不高。本课题的研究就是以此为出发点，在对系统状态输出序列进行时频分析等的基础上，研究不同状态的数理统计规律，并以此建立状态特征量与状态向量、序列长度、策动力幅值、频率等参数之间的数学模型。这样，以状态特征量作为检测统计量，就可得到系统不同状态的定量判据，由此可以提高检测效率和科学性。进一步，将检测统计量与振子阵列或策动力频率控制单元结合，就可以实现对任意频率的信号检测，课题将构建起该过程的完整方法体系。研究是对该问题理论和方法的完善，具有一定参考意义。

强噪声背景下的微弱信号检测是信号处理领域的重要问题。混沌检测技术可以达到很低的信噪比，其检测的核心要先判断系统的状态变化，目前该技术的瓶颈问题是对状态变化的判定大多还停留在相图特征观察等定性分析层面，缺少一个定量判据，导致信号检测方法不能很好有效衔接、不利于计算机程序执行和检测结果可靠性不高。.针对该问题，本项目研究首先立足于解决混沌系统所处状态的定量判定问题。在对混沌系统的输出序列进行数值计算和数值仿真的基础上，通过多种变换域的特征分析，建立了能够定量区分混沌系统三种状态，即混沌态、间歇混沌态和大周期态的状态检测统计量模型，分别是基于庞加莱截面的方差分析统计量模型、基于SFTT的幅时特性统计量模型和类Halmiton系统能量检测统计量模型。这些模型的建立，使得混沌系统的状态分别对应于检测统计量所在的数值区间，这样状态判定的问题就变成了检验检测统计量位于哪个数值区间的问题，极大的方便了计算机程序的执行。结合状态检测统计量模型，项目设计了微弱信号检测的实现方法，有效识别出了信号参数，且能根据要求提高信号参数识别精度。方法中包含对同频信号和非同频信号的处置过程，其中同频信号的频率即为混沌振子策动力频率，非同频信号的频率通过设计策动力频率循环控制单元来实现，找到最大两个检测统计量对应的两个频率中间来获取，幅度参数通过步进改变策动力幅度临界值来获取。.在典型混沌系统Duffing振子的仿真实验中，检测信噪比范围在-30dB以上，未知信号的频率检测准确率在99%以上，幅值检测精度可达0.001。将混沌系统扩展到Duffing-van der Pol振子后，检测信噪比范围在-45dB以上，频率参数识别准确率为98%以上，幅值精度仍为0.001。.项目研究实现了微弱信号混沌检测过程中的无缝闭合，完善了混沌检测理论和方法，并为基于其他混沌系统的微弱信号检测方法提供了借鉴思路。