The 3D similarity coordinate transformation is fundamental and frequently encountered in many areas of work such as geodesy, engineering surveying, LIDAR, terrestrial laser scanning, photogrammetry, machine vision, etc. The algorithms of 3D similarity transformation are divided into two categories. One is a closed-form algorithm that is straightforward and fast. However, it cannot provide the accuracy information for the transformation parameters. The other category of algorithm is iterative, and this can offer the accuracy information for the transformation parameters. However, the latter usually needs a good initial value of the unknown. Considering the accuracy information for transformation parameters is essential or indispensable from the viewpoint of uncertainty, this contribution proposes a weighted total least squares (WTLS) iterative algorithm of the 3D similarity coordinate transformation based on Gibbs vectors. It is fast in terms of fewer iterations, reliable and does not need good initial values of transformation parameters. Two cases including the registration of LIDAR points with big rotation angles and a geodetic datum transformation with small rotation angles are demonstrated to validate the new algorithm.

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The reconstruction methods of marine gravity anomaly encrypted reference map are studied in this study, which can improve the accuracy of underwater gravity matching navigation. Firstly, the mean sea surface as the third dimension component was introduced into the semivariance function of the traditional Kriging two-dimensional (2-D) interpolation method for the first time. After that, a new mean sea surface three-dimensional (3-D) correction method was proposed in order to improve the spatial resolution of the marine gravity anomaly reference map and minimize the loss of accuracy. Secondly, encrypting the spatial resolution of the marine gravity anomaly reference map from 4′×4′, 3′×3′ and 2′×2′ to 1′×1′ as an example, respectively, under the same conditions, the reconstruction accuracy of the new proposed method improved 62.25%, 140.92% and 104.93%, respectively. Thus, compared with the traditional Kriging 2-D interpolation method, we verified that the new proposed method had better reconstruction accuracy. Thirdly, based on the proposed new method, the spatial resolution of the marine gravity anomaly reference map was firstly encrypted from 1′×1′ to 0.25′×0.25′. After that, transforming the spatial resolution of 0.25′×0.25′ into 1′×1′, compared with the original model data of 1′×1′, its the final RMSE is 4.143×10-1 mGal, which further verified the validity and reliability of the new mean sea surface 3-D correction method in application. INDEX TERMS the new mean sea surface 3-D correction method, marine gravity anomaly encrypted reference map, reconstruction accuracy, semivariance function.

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