Shape identification of underwater objects using backscattered frequency signals

The inverse problems in the area of the acoustic scattering often concern the determination of the size, shape, and orientation of an object using the scattered field data. This paper presents a method to retrieve the shape information of an underwater object using illuminated lengths, which can be obtained from the ramp response signatures of the object. An ellipsoidal object submerged in water is considered. Both the low and high backscattered frequency data have been employed to calculate the illuminated lengths. The calculated results show that the illuminated lengths will be more accurate, if only the high-frequency-range data are employed. For ellipsoidal objects, any three illuminated lengths that are not of a same plane can in theory fully determine the shape of the ellipsoid. As the calculated illuminated lengths contain numerical errors, the calculated results of the three semiaxes of the ellipsoid will deteriorate and become unreliable, especially when the three incident directions of the illuminated lengths become close. The reason is that the condition number of the coefficient matrix becomes big in such situations, which leads to an increase of the relative error upper limit in the calculated results. To avoid such errors in close incident wave cases, it is found that the use of more than three incident waves works very well in the shape identification of an underwater object.