Weak Signal Detection Based On The Duffing Chaotic System

With the development of underwater acoustic countermeasure and target stealth technology, the detection technologies of weak underwater acoustic signals face severe challenges. Because of the asymmetry of the seawater medium and uneven interface, the received signals are envelope fluctuation signals. The detection of weak and envelope fluctuation underwater acoustic signals is the most urgent problem to be solved. The research of underwater acoustic signal nonlinear modeling and chaotic detection is of great significance.Duffing chaotic system, which has many merits compared with other detection methods,is a powerful tool in detecting weak underwater acoustic signals. A novel Duffing chaotic system used for processing weak and non-stable underwater acoustic signals is investigated.First of whole, the acquisition of theoretical formula of critical value for abrupt change of the Duffing system is the most urgent problem to be solved. A solving formula of the critical value of Duffing oscillator system is simultaneously obtained by using harmonic balance analysis method. Further detailed, a formula of solving critical value of Duffing oscillator system is given when its internal frequencies is 1rad/s and it could detect weak signals with different frequencies through scale transformation. The simulation results show that the solving formula of critical value for abrupt change is accuracy. Then, in order to detect arbitrary amplitude signals, to reduce the miss probability of misjudgment caused by the total driving force amplitude composed of measured signal and the reference signal less than the critical value for abrupt change, to overcome the shortcomings of qualitative analysis of phase diagram detection methods, quantifiable statistical discrimination results obtained by a reasonable method that combines variable amplitude coefficient Duffing chaotic oscillator with Poincare map set method. At last, a detection method of variable amplitude coefficient short-time Duffing chaotic oscillator array is proposed for the problem of Duffing chaotic system's false positives generated by envelope fluctuation of the signals. The selection principles of short-time window length which must weigh detection precision against computational complexity, are simultaneously proposed on the basis of cross-ambiguity function analysis method. A short-time characteristic window approach to envelope fluctuation signals based on short-time stationarity of underwater acoustic signals is proposed.Periodic extension method is adopted here in order to alleviate the influence of transition and to make the Duffing oscillator system to satisfy the response demand of steady-state. The result of the experiment verify the feasibility of the new approach, which further can improve some existing signal detection methods with Duffing chaotic system.