Accurate estimation of the frequency component is an important issue to identify and track marine objects (e.g., surface ship, submarine, etc.). In general, a passive sonar system consists of a sensor array, and each sensor receives data that have common information of the target signal. In this paper, we consider multiple-measurement sparse Bayesian learning (MM-SBL), which reconstructs sparse solutions in a linear system using Bayesian frameworks, to detect the common frequency components received by each sensor. In addition, the direction of arrival estimation was performed on each detected common frequency component using the MM-SBL based on beamforming. The azimuth for each common frequency component was confirmed in the frequency-azimuth plot, through which we identified the target. In addition, we perform target tracking using the target detection results along time, which are derived from the sum of the signal spectrum at the azimuth angle. The performance of the MM-SBL and the conventional target detection method based on energy detection were compared using in-situ data measured near the Korean peninsula, where MM-SBL displays superior detection performance and high-resolution results.

Passive sonar systems are used to detect the acoustic signals that are radiated from marine objects (e.g., surface ships, submarines, etc.), and an accurate estimation of the frequency components is crucial to the target detection. In this paper, we introduce sparse Bayesian learning (SBL) for the frequency analysis after the corresponding linear system is established. Many algorithms, such as fast Fourier transform (FFT), estimate signal parameters via rotational invariance techniques (ESPRIT), and multiple signal classification (RMUSIC) has been proposed for frequency detection. However, these algorithms have limitations of low estimation resolution by insufficient signal length (FFT), required knowledge of the signal frequency component number, and performance degradation at low signal to noise ratio (ESPRIT and RMUSIC). The SBL, which reconstructs a sparse solution from the linear system using the Bayesian framework, has an advantage in frequency detection owing to high resolution from the solution sparsity. Furthermore, in order to improve the robustness of the SBL-based frequency analysis, we exploit multiple measurements over time and space domains that share common frequency components. We compare the estimation results from FFT, ESPRIT, RMUSIC, and SBL using synthetic data, which displays the superior performance of the SBL that has lower estimation errors with a higher recovery ratio. We also apply the SBL to the in-situ data with other schemes and the frequency components from the SBL are revealed as the most effective. In particular, the SBL estimation is remarkably enhanced by the multiple measurements from both space and time domains owing to remaining consistent signal frequency components while diminishing random noise frequency components.

We contrive a deep learning-based frequency analysis scheme called system-informed neural network (SINN) by considering the corresponding linear system model. SINN adopts the adaptive learned iterative soft shrinkage algorithm as the NN architecture and includes the system model in loss function. It has good generalization with fast processing time and finds a solution that satisfies the system model as a physics-informed neural network. To further improve SINN, multiple measurements are exploited by assuming the existence of common frequency components over the measurements. SINN is examined using simulated acoustic data, and the performance is compared to Fourier transform and sparse Bayesian learning (SBL) in terms of the detection/false alarm rate and mean squared error. SINN exhibits clear frequency components in in-situ data tests, as in SBL, by reducing noise effectively. Finally, SINN is applied to noisy passive sonar signals, which include 43 frequency components, and many are recovered.

We design a simulator in order to seek a surface warship’s survivability against a torpedo attack using MATLAB GUI. Assuming that a torpedo chases a warship in an acoustic-homing way, we model its mobility and detection mechanism according to passive sonar equation. A surface warship manoeuvres into a specified evasive course while deploying static and mobile decoys when a torpedo is detected. Taking a warship’s survival probability as a measure of effectiveness, we perform Monte Carlo simulation by changing four main factors, which include the decoy deployment plan, the torpedo’s initial location, the torpedo’s maximum target detection range, and the mobile decoy’s speed. The simulation results show that using both mobile decoys and static decoys guarantees a higher survival probability than using only static decoys, which depends on their deployment locations and speeds. We further investigate which factors are more likely to affect the survivability via regression analysis, which was based on the simulation results. The regression model results show that torpedo’s detection ability and the speed of mobile decoys highly affect the warship’s survival probability.

In this paper, a four-quadrant Riemann problem for a $2\times 2$ system of hyperbolic conservation laws is considered in the case of delta shock appearing at the initial discontinuity. We also remove the restriction in that there is only one planar wave at each initial discontinuity. We include the existence of two elementary waves at each initial discontinuity and classify 14 topologically distinct solutions. For each case, we construct an analytic solution and compute the numerical solution.