Duffing oscillator is one of the classic nonlinear system that can generate chaotic motion. Given the sensitivity to regular signals but immunity to noise of its chaotic attractor, the Duffing oscillator can be used for weak signal detection. Our recent study on other attractors of Duffing oscillator showed that the state transition of its steady attractor not only has the two major advantages of the chaotic attractor, but also has a specific advantage,that is, it has no transitional zone. In the nearby area of the steady attractor, noise may even cause stochastic resonance, which significantly increases the output signalto-noise ratio. For the first time, we present a measure function for the state transition of the steady attractor of Duffing oscillator and then proposed a novel estimation method for weak sinusoidal signal buried in strong noise.Simulations were conducted to show the efficiency of the proposed method, and results indicate that the proposed method can achieve estimation of amplitude and frequency for sinusoidal signal. Moreover, the proposed method has a higher estimation accuracy and a stronger anti-noise performance than the classical spectrum and maximum likelihood estimation method.
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