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Sailing circle is a commonly used surveying pattern in determining the position of seafloor datum points. In this paper, the positioning efficiency of sailing circle mode is analyzed systematically. Firstly, the acoustic ranging non-differential positioning model considering the variation of sound velocity profile and the inter-epoch differential positioning model weakening the influence of systematic error are analyzed. Then, the positioning efficiency of non-differential and single-difference positioning models in sailing circle mode is analyzed, including the measurability of position parameters, the optimal measurement radius of different component position accuracy, the theoretical accuracy achieved, and the influence of ranging error on positioning parameters, et al. Theoretical analysis shows that in the standard sailing circle mode, to ensure the accuracy of different components of the datum position, different optimal measurement radiuses are derived, and the elevation component cannot be estimated with the pre epoch and post epoch differential positioning model. Both the simulation data and the measured examples show that the differential positioning model in sailing circle mode weakens the influence of the ranging system error, but also reduces the geometric observation intensity of the design matrix, which even lead to an ill-posed model and obvious weakening of the depth information estimation accuracy of the differential model.

To solve the problem of seafloor control point (transponder) absolute positioning with a large deviation of the vertical solution, this paper proposes a differential localization algorithm with depth difference and horizontal distance constraint between underwater control points. Firstly, the variation of sound velocity profile is studied. Based on this conclusion, the influence of uncertain sound velocity profile on the ranging error is analyzed. Secondly, according to the change law of ranging error, the corresponding measuring line is designed. And an underwater differential localization algorithm for this survey strategy is proposed. Finally, simulation experiments show that the deviation of the vertical solution is reduced from more than 30 cm to about 10 cm. It implies that the new method can effectively reduce the deviation of the vertical solution of the control point positioning compared with the traditional method (circular sailing).

This paper focuses on solving the problem of seafloor control point absolute positioning with low vertical accuracy based on the survey ship sailing circle. The method of dealing with the systematic error based on semi-parametric adjustment model was proposed. Firstly, the influence of sound speed change on ranging error is analyzed. Secondly, a semi-parametric adjustment model for determining three-dimensional coordinates of underwater control points was established. And respectively proposed solutions under two different conditions, the observation duration is an integral multiple or non-integer multiple of the long-period term of the ranging error. Simulation experiment results show that this method can obviously improve the accuracy of vertical solution of seafloor control point compared with difference technique and least square method when internal waves exist and observation duration is less than an integer multiple of the long-period term of the ranging error.

The coordinates are obtained from observations by using least-squares method, so their precision should be contaminated by observation errors and the covariance also exists between common points and non-common points. The coordinate errors don't only exist in the initial frame but also in the target frame. But the classical stepwise approach for coordinate frame transformation usually takes the coordinate errors of the initial frame into account and overlooks the stochastic correlation between common points and non-common points. A new rigorous unified model is proposed for coordinate frame transformation that takes into account both the errors of all coordinates in both fame and inter-frame coordinate covariance between common points and non-common points, and the corresponding estimator for the transformed coordinates are derived and involve appropriate corrections to the standard approach, in which the transformation parameters and the transformed coordinates for all points are computed in a single-step least squares approach. The inter frame coordinate covariance should be consistent to their uncertainties, but in practice their uncertainties are not consistent. To balance the covariance matrices of both frames, a new adaptive estimator for the unified model is thus derived in which the corresponding adaptive factor is constructed by the ratio computed by Helmert covariance component estimation, reasonable and consistent covariance matrices are arrived through the adjustment of the adaptive factor. Finally, an actual experiments with 2000 points from the crustal movement observation network of China (abbreviated CMONOC) is carried out to verify the implement of the new model, the results show that the proposed model can significantly improve the precision of the coordinate transformation.