In the paper, we analyse the basic dynamical model of the chaotic oscillator by using the theory of intermittent chaos to construct the column of the intermittent chaos, and present an effective method to detect the weak underwater acoustic signal with an unknown frequency. Duffing oscillator is sensitive to phase transformation from chaos to intermittent chaos, whose frequency difference is slightly different from that between the driving force signal and the signal to be detected. By employing this theory, we detect the frequency of the ship signal in ocean background noise. For the detection by using the intermittent chaos, there exists no effective way to estimate the frequency of the signal to be detected, which can only be judged by empirical methods and therefore the man-made error will exist. All of these will affect the consequence of the intermittent chaos and make the practical application difficult. To solve this problem, in this paper, we first study the basic theory of the chaotic system, then construct the simulated signal to examine the system, and finally detect the ship signal. To make the detection feasible, a chaotic oscillator column is considered to sweep through the unknown frequency of the signal. By using this method, we can obtain the frequency range. Finally Hilbert transform is used to detect the envelope of the intermittent chaos followed by measuring the frequency of the envelope through using Fourier spectrum. Thus the frequency of the signal can be calculated by using the function describing the relationship among the driving force signal, ship signal and the envelope. The simulations and the detection processing of the measured acoustic signal are carried out by using the proposed method, which can effectively detect the frequency of the ship signal embedded within strong background noise and also the frequency of the signal to be detected can be calculated, which is conducive to solving the presently existing problem about frequency estimation. Signal-to-noise ratio can be enhanced by 4.4 dB based on the method by using the Hilbert transform compared with by using the method just through using an intermittent chaotic oscillator column, which verifies the effectiveness of the method in this paper.
