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.