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本文研究了混沌Duffing振子在弱信号检测系统中表现出的统计特性,说明了Lyapunov指数的统计特性与弱信号检测和估计之间的关系.之前的一些研究表明,混沌系统可以用于弱信号的检测,并将Lyapunov指数作为判定混沌状态的确定性依据.但本文的研究工作表明,弱信号检测系统中的Lyapunov指数存在一定的统计特性,将其作为信号检测判据需要考虑更多因素.因此,本文从理论上分析了混沌弱信号检测系统的Lyapunov指数存在的统计特性,并利用仿真数据建立了统计模型,确立了混沌检测系统的虚警概率和检测概率的计算方法.进而推导出了策动力阈值门限的选取公式和弱信号检测信噪比,给出了信号幅度估计的方法.实验结果表明,混沌弱信号的检测和估计性能与采样时间和采样间隔密切相关,可以采用统计信号检测的理论来衡量其性能.
In this paper, we study the statistical properties of chaotic Duffing oscillator in weak signal detection system, and show the relationship between the statistical properties of Lyapunov exponents and weak signal detection and estimation.Previous studies show that chaotic systems can be used in weak signal And the Lyapunov exponent is taken as the determinant basis for judging chaos.However, the research work in this paper shows that the Lyapunov exponent in weak signal detection system has certain statistical properties, and more factors need to be considered as the signal detection criterion.Therefore, , This paper analyzes the statistical characteristics of the existence of Lyapunov exponents in the chaotic weak signal detection system theoretically and establishes a statistical model by using the simulation data to establish the calculation method of the false alarm probability and the detection probability of the chaotic detection system.Furthermore, Power threshold threshold selection formula and weak signal detection signal-to-noise ratio, and gives a method of signal amplitude estimation.The experimental results show that the detection and estimation performance of chaotic weak signal is closely related to sampling time and sampling interval, which can be detected by statistical signal Theory to measure its performance.