On detectability of a ship's Kelvin wake in simulated SAR images of rough sea surface

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.