The positioning method based on single beacon ranging is the further development of the underwater acoustic positioning technology. In this paper, the location of single beacon ranging based on the straight path is studied. On one hand, the conventional direct reduction method is not applicable to the straight path. On the other hand, when the beacon is in the straight line or the extension of the straight line, the linear iterative algorithm can not locate the carrier. When the coefficient matrix is almost singular or bad condition, the error of the solution will obviously increase. In this paper, an improved algorithm is proposed to solve the problems existing in the solving method, which can overcome the influence of singular or bad condition of coefficient matrix. Simulation results show that the localization accuracy of the proposed algorithm is similar to that of the Gauss Newton method in most cases. This algorithm can also realize the positioning calculation when the beacon is in the straight line or the extension of the straight line. This algorithm can obviously improve the positioning accuracy where the positioning accuracy is not high when using the linear iterative algorithm. The effectiveness of the proposed algorithm is verified by experiments on the sea.
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