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Passive diver detection is really significant as it constitutes a potential real-time monitoring of serious underwater threats. Up to now, there is still a lack of an efficient approach to characterize the complexity and fickleness with non-parametric and non-information priors. To achieve an improvement, a phase trajectory entropy method is proposed that should be promising. A coarser-grained distribution is created during entropy counting. The value of phase trajectory entropy is demonstrated by simulation and applied to real recorded data. The results show that phase trajectory entropy method considerably outperforms narrowband energy detection and the bubble entropy method.

Passive target detection under low signal-to-noise ratio is essential in various underwater circumstances, but difficult as lacking of targets’ prior information, special propagation characteristics and effect of background noise. Based on the time–frequency representation, we develop a narrow band time–frequency space matched method. The time–frequency matrix is derived based on the ray theory, the warping expression, and the pooling function. Then the sliding cumulative convolution of the matrix obtains a higher signal to noise ratio output. The likelihood ratio test detector is derived for passive target detection. Analysis and the ocean experiment results show that the proposed approach outperforms other passive detectors.

The principle of underwater acoustic signal propagation is of vital importance to realize the “digital ocean”. However, underwater circumstances are becoming more complex and multi-factorial because of raising human activities, changing climate, to name a few. For this study, we formulate a mathematical model to describe the complex variation of underwater propagating acoustic signals, and the solving method are presented. Firstly, the perturb-coefficient nonlinear propagation equation is derived based on hydrodynamics and the adiabatic relation between pressure and density. Secondly, physical elements are divided into two types, intrinsic and extrinsic. The expression of the two types are combined with the perturb-coefficient nonlinear propagation equation by location and stochastic parameters to obtain the stochastic nonlinear differential propagation model. Thirdly, initial and boundary conditions are analyzed. The existence theorem for solutions is proved. Finally, the operator splitting procedure is proposed to obtain the solution of the model. Two simulations demonstrate that this model is effective and can be used in multiple circumstances.

A stochastic nonlinear ray propagation model is proposed to carry out an exploration of the nonlinear ray theory in underwater signal propagation. The recurrence plot method is proposed to quantify the ray chaos and stochastics to optimize the model. Based on this method, the distribution function of the control parameter δ is derived. Experiments and simulations indicate that this stochastic nonlinear ray propagation model provides a good explanation and description on the stochastic frequency shift in underwater signal propagation. Major State Basic Research Development Program of China https://doi.org/10.13039/501100012336 RF Goverment Grant National Nature Science Fundation of China

In the marine environment, when the line spectra of underwater target radiated signal are unknown or the continuous spectra are weak, it is extremely hard to accurately detect the underwater weak target. The line spectrum based method commonly requires spectrum information for detection, and the continuous spectrum based energy method is hard to achieve accurate detection in long distance. In this paper, an underwater radiated noise detection method based on generalized Duffing oscillator detection system is proposed. Firstly, a generalized Duffing oscillator detection system for non-periodic and non-stationary input signal is proposed through deducing the traditional Duffing oscillator detection system that is perturbed by periodic signal. And the proposed generalized Duffing oscillator detection system is able to detect the signals of targets without needing prior information. Secondly, when the target radiated signal (non-periodic and non-stationary signal) is input into the generalized Duffing oscillator, a special form of output phase space (a special state of motion) is discovered and the differences in output phase space among different input signals (periodic stationary signals, nonperiodic non-stationary signals and the target radiated signals) are analyzed. It is found that the special phase space has different form from the output phase spaces of other kinds of signals; accordingly the underwater targets can be detected through the representation of the difference between special phase space and ordinary phase space. Thirdly, a discrete distribution sequence calculation method based on phase space is proposed for the precise and efficient judgment of system motion. The proposed calculation method defines a similar-grid function, based on which, the distribution sequence calculation method of output phase space is deduced, and the distribution sequences of different kinds of output phase spaces are calculated. The method realizes an embedded expression of system output by using the statistical complexity, therefore achieving the embedded underwater target detection when the line spectra of underwater target radiated signal are unknown or the continuous spectra are weak. The analysis result indicates that the method is of low-computation. Finally, the experimental results in the sea are described and the lowest signalto-noise ratio (SNR) of the method is calculated to be -9.133 dB. Simulation and experimental results have shown that the proposed method can detect target successfully in a lower SNR than traditional detection method, and the real-time performance can meet the demand for underwater detection. The method in this paper provides new ideas and ways of thinking for underwater target detection, and has very important reference value for low SNR long-distance target detection under real condition.