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The Kelvin ship wave generated by the thin ship. (a) Gray image of ship wave (unit: m). (b) Three-dimensional fluctuation of ship wave.
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The composite backscattering of the ship model on sea surface is investigated with the spilling breaking waves and ship bow waves. The spilling breakers are approximately modeled with the wedge-like waves, and the ship bow waves are simulated based on the Kelvin model. With the modified four-path model, each scattering component is evaluated with t...
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... stern wave ζ K 0 (x + L, y), and f is the viscosity coefficient. As shown in Figure 3, the Kelvin ship waves are modeled with thin ships. We build the sea surface with the spilling breakers and the ship bow waves firstly, the details of the model meet Ref. [29], here the scale grid of surface is set to 1×1 m 2 and the sea surface area is 100×100 m 2 . ...
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Citations
... The MEC is based on the fact that a limited result can be obtained by the radiation integral of scattering field of any limited distribution of currents in far zone. The equivalent currents are assumed to exist on the edge of the loop, and the target scattering field is expressed as [20] ...
... Seeking efficient and accurate solution to the electromagnetic composite scattering from targets on sea surface has attracted much interest [1][2][3][4][5], which has found extensive applications in oceanic communication, radar surveillance and target detection, etc. In the analysis of composite scattering from ship-sea geometries, different numerical methods have been developed in recent years, such as the method of moment (MoM) [6][7][8], finite element method (FEM) [9] and finite difference time domain (FDTD) [10,11]. ...
This paper presents a hybrid scheme for fast calculation on the bistatic composite scattering from electrically very large ship-sea geometry at high frequencies. Based on the Kirchhoff approximation (KA), we try to break the large-scale sea surface into myriads of plane facets, then derive the Kirchhoff integration analytically on each individual discretized facet. The analytical expression obtained, so- called the " facet-based Kirchho® approximation (FBKA)", is suitable for a quick scattering calculation on the electrically very large sea surface, since it is beyond the intensively refined meshes as the usual Monte Carlo implementation does. Meanwhile, combined with graphical electromagnetic computing method (GRECO) to extract the illuminated and shadow facets in accordance with the incident direction, the conventional physical optics method (PO) is improved by employing current marching technique (CMT) to calculate the currents in the shadow region. The shadow-corrected GRECO is presented in this hybrid model to solve the bistatic scattering from complex and very electrically large perfectly electric conducting (PEC) objects. The accuracy of the shadow-corrected GRECO is con-rmed well by exact numerical methods, especially at large scattering angles. The electromagnetic interactions between the ship and sea surface are estimated by the famous " four-path model", which has been proved to be valid for ship scattering at relatively calm sea state. Several numerical examples have been presented to demonstrate the e±ciency and accuracy of the proposed hybrid method.
... Най-разпространени са алгоритмите с осредняване на стойността на елементите в обучаващия прозорец -CA (cell averaging) и MLD (mean level detector) [80,131,185,194,208,212,233,245]. Те са ефективни при откриване на сигнали на фона на еднородни и стационарни смущения. ...
In this book, several advanced detection algorithms for Track-Before-Detect (TBD) procedures using the Polar Hough Transform (HT) are proposed and studied. In real radar applications, however, when the two target parameters, range and azimuth, vary in time, the PHT can be successfully used because in that case the input parameters of the PHT are two polar coordinates of a target – range and azimuth. Such advanced structures of the TBD using the PHT have been developed and studied in the book. The PHT is analogous to the standard HT and performs all the data collected for several previous scans into a single large multidimensional polar data map. The general structure of an adaptive Polar Hough detector with binary integration is similar to that of a standard Hough detector. The Polar Hough transform maps all points from the (range-azimuth) space into the Hough space of patterns. The association with a particular pattern is done by thresholding the Hough parameter space with a predetermined threshold. In order to enhance the target detectability in conditions of Randomly Arriving Impulse Interference (RAII), a CFAR processor is proposed to be used for signal detection.
In this book, it is assumed that the noise amplitude is a Rayleigh distributed random variable and therefore the noise power is an exponentially distributed variable. Different Hough detectors that employ CFAR processors such as Cell Averaging (CA), Excision (EXC), Binary Integration (BI), Excision with Binary Integration (EXC BI) for signal detection in the (r-a) space are studied and compared in the book. The structure of these Hough detectors includes the following operations - CFAR signal detection in the area of observation and the PHT of the target range measurements from the observation area into the Hough parameter space, binary integration of data in the parameter space and, finally, linear trajectory estimation. The results obtained show that different CFAR processors work successfully in combination with a Hough detector in conditions of RAII, and allow to evaluate the parameters of the targets. The detection probability of a Polar Hough detector is calculated by Brunner’s method as for a standard Hough detector. The use of the PHT instead of the standard HT allows detecting target trajectories in real situations when targets move at variable speeds along arbitrary linear trajectories.
The TBD approach that applies the HT to multi-sensor detection in conditions of intensive RAII is proposed in the book. As usual, the fusion center of a decentralized system applies binary integration of the data received from each sensor. In such a system, at the first stage, radars produce local decisions by the TBD-PHT processing and at the second stage - all the local decisions are transferred from radars into the fusion node where coordinates and time are associated in the Global Observation Space (GOS). The centralized system, however, firstly associates data with common coordinates and time received from sensors and then performs them by the TBD-PHT processing. In this context, two variants of a centralized asynchronous net with association of signals or signal detections are developed and analyzed. The algorithm with association of signals includes two stages. At the first stage, the signals received from sensors are non-coherently accumulated in the signal matrixes of the fusion centre, because the size of signal matrixes and their cells are the same for the entire radar net. At the second stage the accumulated signals are transferred into the GOS. The algorithm with association of signal detections firstly accumulates decisions for signal detection after CFAR processing in each sensor, secondly - transfers detections in the GOS. The expressions for calculating the probability characteristics, i.e. the probability of target detection, trajectory estimation and the false alarm probability, are derived under the assumption that both target coordinates (range and azimuth) and both parameters of the Hough parameter space ρ and θ are measured with or without errors. The results obtained show that the detection probability of multi-sensor centralized TBD-PHT processors is higher than that of the decentralized detectors. The performance evaluation of multi-sensor TBD-PHT processors has been carried out by Monte-Carlo simulations in MATLAB computing environment. The DPA based Hough detector is close to the potential of the most effective multi-sensor CSA Hough detector. The target coordinate measurement errors in the (r-t) space mitigate the operational efficiency of multi-sensor Hough detectors. The needed operational efficiency requires the appropriate sampling of the Hough parameter space.
The book includes the following chapters: 1. Straight Lines and trajectories Detection Using Hough Transform; 2. Trajectories Detection Using Polar Hough Transform; 3. Probability characteristics of CFAR Hough detectors in the presence of randomly arriving impulse interferences; 4. Multi-sensor (multi-channel) data association using polar Hough transform.
... Through the inversion of the radar scattering cross sections, physical states of the ocean surface can be provided, such as current vectors, waveheight spectra, wind information, etc. Therefore, intensive investigations have been done during the past several decades [7][8][9][10][11][12][13][14][15][16][17][18][19]. The sea-echo Doppler spectrum has been observed and explained to be "Bragg scatter" in [7], which is the same phenomenon with the scatter of X-rays in crystals. ...
... We spread out the normal vector of the rough surface with the perturbation method, and take k 0 f 2 , @f 2 =@x, @f 2 =@y as perturbation references. Then, substituting the low-order formula into the boundary condition (11), (12), two new boundary conditions can be obtained and given by: ...
The higher order Bragg scatter from rough surface, which belongs to an electromagnetic scatter, is investigated with the boundary perturbation method. The equations of radar scatter cross sections for higher order Bragg scatter are deduced. The performance of higher order Bragg scatter is distinct from the sea-echo spectra in real data when at high sea states or in the upper part of the HF band. The accuracy and efficiency of the deduced formulas are compared and validated with several examples of the Ocean State Measuring and Analyzing Radar-S experiments data, which were obtained in different locations and at different operating frequencies.
... The scattered wave vector is K es = e +q eẑ , where k e and q e are appropriate components of the scattered wave vector, respectively. q 0 and q can be expressed as [33,34]: ...
The ship Kelvin-wake models on two-dimensional (2-D) linear and nonlinear sea surfaces are combined with the second-order small-slope approximation method (SSA-II) to comparatively study the corresponding electromagnetic (EM) scattering characteristics. The nonlinear sea-surface models include the Choppy Wave Model (CWM) and the second-order Creamer model (Creamer (2)). Considering the limitations of using the ideal plane EM wave incident upon a rough sea surface of the limited size, the modified tapered wave is utilized as the incident wave to derive the scattering waves. Due to the fact that the nonlinear effects of Creamer (2) surfaces is obviously stronger than those of CWM surfaces, the bistatic normalized radar cross section (NRCS) calculated from Creamer (2) surfaces is significantly greater than that of its linear and CWM surfaces for scattering angles departing from the specular direction, and the backscattering coefficients from Creamer (2) surfaces are also the greatest except within quasi-specular (near vertical incidence) region. Moreover, for the linear and nonlinear sea surfaces, the influences of different wind speeds and directions on scattering characteristics are also calculated and analyzed in detail. However, taking the ship Kelvin wakes into account, the corresponding scattering features are obviously distinct from those of the single linear and nonlinear sea surfaces. This helps to provide a basis to extract the related ship information through the scattering characteristics of ship Kelvin wakes. Also it shows that the small-slope approximation method is a very effective analysis method to deal with the EM scattering from the rough sea surface.
... The study of electromagnetic (EM) scattering from sea surfaces is an old but vigorous research realm. Stochastic waves can be used to form a rough sea surface, and has been widely applied to the research areas such as oceanic surveillance, target detection [1][2][3][4][5][6][7][8], remote sensing and so on [9][10][11][12][13][14][15]. But the fractal sea surface is also a very good tool for characterizing the natural sea surface as a result of its semi-stochastic and semi-periodic features [16,17]. ...
In this paper, a one-dimensional nonlinear fractal sea surface model has been established based on the narrow-band Lagrange model, which takes into account the vertical and horizontal skewnesses for the sea surface. By using the method of second-order small-slope approximation (SSA-II), the normalized radar cross section (NRCS) and Doppler spectrum of linear and nonlinear fractal sea surface are calculated. The calculated NRCS of the nonlinear fractal sea surface is larger than the linear surface for backscattering, especially for large incidence angles, which indicates the nonlinear surface has stronger scattering echoes. And the result of nonlinear fractal sea surface is also larger than the linear fractal sea surface for bistatic case, which is characterized as the discrepancies being small near specular direction, while the discrepancies becoming larger as the scattering angles departing from the specular direction. For the Doppler spectrum of sea surface, the nonlinearity of sea surface effects greatly enhances the Doppler shift and the Doppler spectrum bandwidth at large incidence angles, which are attributed the fact that the nonlinear-wave components propagate faster than the linear-wave components and the nonlinear fractal sea surface corrects the phase velocities by adding the horizontal and vertical skewness. And also, all the results can indicate the validity of this nonlinear model.
... The scattered wave vector is K s = +qẑ, where k and q are appropriate components of the scattered wave vector, respectively. q 0 and q can be expressed as [29,30]: ...
Electromagnetic (EM) scattering properties from the ship wakes on the two-dimensional (2-D) perfect electric conductor (PEC) sea surfaces are studied by utilizing the small-slope approximation (SSA) theory. Considering the limitations of using the ideal plane EM wave incident upon a rough sea surface of the limited size, the expressions of the scattered field and scattering amplitude are derived by utilizing the modified tapered incident field. Based on a simplified segmented ocean spectrum model, the bistatic and monostatic normalized radar cross sections (NRCS) from the PEC sea surfaces with and without ship wakes are calculated, respectively. Meanwhile, the variation of scattering coefficient as scattering angles is given and compared under different polarization states. The results show that the scattering from the PEC sea surfaces with ship wakes is evidently different from that without them in bistatic and monostatic scattering. This provides a basis to extract ship wake characteristics. Also it shows that the SSA is a very effective analysis method to deal with the EM scattering from the rough sea surface. Finally, the effect of different tapered factors on backscattering coefficient is discussed, and it is concluded that an artificial reflection from the boundaries and a scattering upwarping from low-grazing incidence can be avoided just when the tapered factor is relatively smaller. This gives the theoretical basis for the analysis of EM scattering characteristics of ship wakes on the PEC sea surface.
The study on the scattering mechanism of breaking ship waves provides important theoretical basis to the ship detection and radar imaging in a marine environment. This paper presents a new procedure for evaluating the electromagnetic scattering field of breaking ship waves over a perfect electric conductor sea surface. In this paper, different forms of the near-field ship waves are obtained by the computational fluid dynamics (CFD) method, which provides a new means of analyzing a fully coupled fluid-structure interaction system in a detailed manner. Sufficient grids are used in the CFD numerical simulation to obtain the flow field information of the breaking waves. The accuracy of the breaking wave geometry has been improved obviously, which will lead to a better understanding of the electromagnetic scattering characteristics of breaking ship waves. Considering the multiple scattering between the ship hull and the breaking waves, the scattering field of the sea surface and the ship hull are evaluated by the forward-backward iterated physical optics algorithm. Both scattering characteristics of the breaking ship waves and distribution of the scattering coefficients are obtained. By comparing the bistatic scattering field in different situations, the numerical results show some important effects of the breaking ship waves, which are quite different from the effects of ship models. What is more, the time varying radar cross section of the breaking ship waves are presented based on the dynamic ship waves.
