Iterative Algorithm of Seafloor Control Points Positioning Taking Reference Depth Error into Account

Objectives The measurement of three-dimensional absolute coordinates of high-precision seafloor control points is a key step in the construction of seafloor geodetic control network. The underwater positioning method based on the navigation of the survey ships is an important method to solve this problem. However, the measuring routes are spatially limited, which result in less accurate solutions for the vertical coordinates of the control points. To solve this problem, we improve the coordinate calculation meth‍od, and use the vertical solution correction value to correct the reference depth information during the iterative process, which improved the accuracy of the slant distance calculation, so that the purpose of improv‍ing the accuracy of the vertical solution is achieved.

Methods First, the concept of the position line with the same propagation time is introduced. Based on this concept, the influence of the error of reference depth on the calculation of slant range is analyzed. Then the model convergence process of control point positioning under different error relationship curves is analyzed. The position relationship between the reference depth and the real water depth is determined according to the positive or negative of coordinate correction value. Finally, the vertical coordinate correction value is used to correct the reference depth information, so that the accuracy of vertical solution is improved.

Results The experimental results show that: (1) When the gradient value of the errors relation curve is not zero and there is no error in the sound velocity profile, the traditional method is affected by the reference depth error, so that the error of the vertical solution of the control point coordinate is an order of magnitude higher than that of the horizontal solution. While the new method is almost unaffected. (2) The sound velocity error has little effect on the horizontal solution and a large effect on the vertical solution, and increases with depth. (3) The reference depth error is coupled with the sound velocity error, which further increases the vertical solution error. The new method can reduce the coupling effect.

Conclusions When the gradient value of errors relation curve is zero, the reference depth error causes little change on the positioning result. When the gradient value of errors relation curve is not zero, the reference depth error increases the vertical solution error. The new method can reduce the impact of the reference depth error on the positioning of seafloor control point, and weaken the coupling effect of the sound velocity error and the reference depth error.