应用非线性微分方程组实现弱信号检测

Detection of a Weak Signal by Using a Group of Nonlinear Differential Equations

为了检测相位随机分布的微弱正弦信号,提出了采用非线性微分方程组的检测方法。N个方程的策动力初相等间隔设置,每个方程均设置在临界混沌状态,将被检测信号加入到各方程中进行运算,当相位随机分布的微弱正弦信号出现时,至少有一个方程会进入周期态从而检测出信号。利用Mel'nikov定理证明了该方法的可行性。数值实验表明利用16个方程同时检测能将信噪比为-90dB的随相弱正弦信号检测出来。

In order to detect the phasely random weak sinusoidal signal, a new method of using a group of nonlinear differential equations to realize the detection is presented. The intervals of the initial phases of the driving forces are set equal, every equation is set in critical chaotic state, add the signal to be detected into every equation, when the phasely random weak sin signal does appear, at least one of the equations will go into periodical state thus the signal is detected out. The feasibility of this method is proved using Mel'nikov theorem. Computer simulation indicates that the phasely random sin signal whose SNR = -90 dB can be detected out by using 16 nonlinear differential equations.