Frequency Estimation for Weak Signals Based on Chaos Theory

The method of the weak signal detection using the Duffing oscillator´s initial conditions sensitivity was analyzed, and the Melnikov method of determining chaotic threshold of Duffing oscillators is discussed. The principle of weak signal detection based on the change of phase trace is described, and the influence of noise to the system status in the chaos detection process is also studied. Simulation experiments show that the oscillator is sensitive to the small signal having the tiny frequency difference with the referential signal and immune against the random noise and interference signal having larger frequency difference with the referential signal. Through analyzing the intermittent chaos mechanism of Duffing oscillator, it was found that the system output is a intermittent chaotic signal when input frequency deviates the compulsory drive frequency slightly, and the deviation can be estimated by the statistic characteristic of output chaotic signal. Simulation results show that the signal with low SNR can be detected by the method.