联合增益递推的Duffing系统弱信号检测算法

相变判别在Duffing振子弱信号检测中具有至关重要的作用,传统的判别算法复杂度高而精度低,限制了Duffing振子的应用,因而需要寻求更优的判别算法.本文通过欧拉方程建立正弦策动力Duffing振子的状态方程,并对Duffing系统进行滤波估计,推导出系统扩展卡尔曼增益的递推表达形式,以此为据提出了一种联合卡尔曼增益递推方程判别Duffing系统状态的新方法,同时根据增益随信号幅度变化的规律,提出了运用联合系统对弱信号进行定性和定量检测的方法,仿真验证表明,该方法可有效地对弱信号进行检测,相比传统Lyapunov指数判别法,运算耗时降低了两个数量级,且运算精度得到了显著提高.

A Weak Signal Detection Method by Duffing System with the Gain

The identification of phase transition plays an important part on the detection of the weak signal by Duffing oscillator.Traditional identification algorithm has the complicated calculation and the low precision,which confine the applications of Duffing oscillator,so it’s necessary to seek a better identification algorithm.In the paper the state equation of Duffing using sine function as the driving force is set up by the Euler-maruyama algorithm.In the filtering process of Duffing with extended Kalman filter,the recursion expression of Kalman gain is derivated,then a new method associated with the gain to identify the phase transition of Duffing is offered,and meanwhile,according to the transition of Kalman gain with the amplitude of signals,the method of weak-signal detection with the joint system is offered.The simulation shows that the method can effectively detect the weak signals.Compared with the Lyapunov identification method,the simulation time of the new algorithm falls two orders of magnitude,and the precision of the calculation improves remarkably.