On Detectability of a Ship's Kelvin Wake in Simulated SAR Images of Rough Sea Surface

Abstract

Synthetic aperture radar (SAR) images of ship wakes frequently exhibit long streaks. Some of the streaks are attributed to the Kelvin V-wave wake, and others are attributed to the turbulent and bright narrow V-wake. Ocean waves reduce the detectability of Kelvin wakes in SAR images. The SAR imaging of Kelvin wakes of two ships with different dimensions moving in rough sea is studied theoretically. The Kelvin wakes are simulated using the Michell theory. The random sea surface is simulated using the Pierson-Moskowitz type wave spectrum. The elevations of the points of the water surface and their velocities and accelerations are considered as a superposition of a ship's coherent waves and wind waves. A two-scale composite model and the velocity-bunching integral are used to simulate the intensity of SAR images of a disturbed sea surface with an embedded Kelvin wake. The fast discrete Radon transform is applied to detect the boundaries of the simulated Kelvin wakes. The probabilities of missing detections (PMD) and false alarms (PFA) are estimated numerically. The influence of ships, wind, and SAR parameters on PMD and PFA is discussed. It is illustrated that PMD/PFA strongly depend on the sea state. Index Terms-Probability of false alarms (PFA), probability of missing detections (PMD), Radon transform (RT), sea waves, ship wake, synthetic aperture radar (SAR).

Application of Facet Scattering Model in Sar Imaging of Sea Surface Waves With Kelvin Wake

“…Therefore, it is necessary to discuss the influence on radar image under different traveling directions of a ship, as is illustrated in Figure 10. The sea surface is generated at wind speed of 3.0 m/s and ϕ s is Figure 11 shows two SEASAT L-bands HH polarized SAR images under different ship travel directions under low to moderate wind speeds [15]. Regardless of the turbulent wake appearing as a narrow dark streak along the ship track, it is evident in Figure 11 The wake characteristic is shown more obvious by ship 4 and ship 5 in Figure 11(b), both of which are moving with an angle of ϕ s = 228 • relative to the radar look direction.…”

“…Since the formulation of fluid dynamic theory was firstly concluded mathematically by Lord Kelvin, there have been a lot of scholars to do researches focusing on the Kelvin wakes [7][8][9][10][11][12][13][14][15]. Based on the Bragg mechanism of sea surface, Tunaley et al [7] researched the SAR imaging of ship wakes in L-band and analyzed its validity through a comparison with the SeaSAT SAR imagery.…”

“…Recently, ArnoldBos et al [13] developed a bistatic, polarimetric radar simulator for estimating pseudo-raw radar echoes of ship wakes that can be further processed for bistatic SAR (BiSAR) imaging. The detectability of the boundaries of Kelvin wake in SAR images is studied with the application of discrete Radon transform by Zilman et al [15].…”

Ship Wake Detection in SAR Images via Sparse Regularization

“…In this paper, we assume priors to be of exponential form as, p(X) ∝ exp{−λψ(X)}. Thus, the cost function in (8) becomes…”

Wake Component Detection in X-Band SAR Images for Ship Heading and Velocity Estimation

“…In this ambit, ship wake detection not only has strong interest as the validation of ship presence, but also generates data useful for ship route estimation. In fact, if wake direction provides information about ship heading, methodologies have also been developed to derive ship velocity from additional wake-based information [11][12][13][14][15][16].…”