Precise positioning of a transponder placed on a sea floor. 3. Improvement of convergence of iteration calculation

The precise positioning of a sea bottom transponder is very important for measuring the sea bottom crustal movement. In the previous papers, it was 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. However, the convergence of iteration calculation was a weak point of the previous theory. In the present paper, this problem is reexamined from the basic point. This problem is a singular one that does not converge to a unique solution. A method to eliminate the singularity is proposed. In the previous theory, only the Newton-Raphson method was used to solve the nonlinear equation by iteration. In the present paper, a hybrid method consisting of Monte Carlo and Newton-Raphson methods is introduced. The stability of the calculation seems to be improved considerably.