Abstract
In the previous papers, it is shown that not only the position of a bottom transponder but also the underwater acoustic velocity distribution can be determined, if the position of surface transponders and ranges between the surface and bottom transponders are known. Also, a theoretical possibility was shown that the position of the bottom transponder can be obtained in the order of centimeters by using equipments available now. They were extended to three-dimensions in the third paper. More realistic results were obtained there. In the present paper, the theory is extended to include the effects of current. The basic nonlinear equations are obtained by a variational principle. Some two-dimensional numerical calculations are conducted, and the convergence of the iteration calculations is verified. The numerical results show that the effects of current can be obtained and can't be neglected for precise positioning.
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