Multi-Frequency Weak Signal Detection Using A Modified Duffing Chaotic System

The Duffing chaotic system serves as an excellent tool for detecting single frequency weak signals obscured by strong noises, but exhibits poor performance when it comes to the multi-frequency case which is pervasive in numerous engineering applications. By introducing a nonlinear damping term into the original system, this paper establishes an enhanced Duffing chaotic system to surmount this issue whose minimum detectable Signal-to-Noise Ratio (SNR) is largely improved compared with that of the traditional Duffing chaotic system. Based on the Poincar´e map, a quantitative phase state judgment method is proposed to reduce the computational complexity required for phase state determination, and an automatic multi-frequency weak signal detection method is finally formulated by further resorting to a frequency shift module. Experiment results show that this proposed method can detect multi-frequency weak signals with an SNR of -31 dB with the maximum frequency measurement relative error of 0.15%, showing the effectiveness and advantage of the proposed weak detection method.