A Nonlinear Gauss-Helmert Model and Its Robust Solution for Seafloor Control Point Positioning

Abstract Using GNSS-Acoustic (GNSS-A) technology to establish the seafloor geodetic datum is both feasible and flexible and thus has become an important way to obtain the absolute positions of seafloor control points. However, numerous errors are inevitable in marine surveying, including systematic errors and gross errors caused by GNSS dynamic positioning, inaccurate sound velocity profile measurements, and ocean ambient noise, and their interference will be directly reflected in the positioning results. To accurately calculate the seafloor control point coordinates, this paper first notes that the general error propagation law (EPL) method is defective in dealing with various error factors in GNSS-A positioning. A more rigorous method incorporates the time-varying term of the sound velocity ranging error into the coefficient matrix of the underwater observation equation, and the transducer position error should be considered. Therefore, a Gauss-Helmert (GH) model is used for seafloor control point positioning. Then, considering the dual nonlinearity of the model, a Lagrange objective function is constructed to derive its solution algorithm. On this basis, considering the gross errors polluting of the observations, the robust estimation principle is introduced, and the robust solution steps are given. Finally, simulation experiments and a testing experiment in the sea area near Jiaozhou Bay are used to verify the performance of the new method. The results show that the functional relationship and stochastic model of the nonlinear GH model for seafloor point positioning are reasonably described. Under ideal conditions with no gross errors and either different water depths or different transducer position errors, the accuracy and stability of the new method are both higher than those of the EPL method. When the observations are polluted by gross errors, the robust algorithm of the new method can accurately identify the abnormal information. By improving the robustness of the observation and structure spaces, the positioning precision of the 3D point deviation results can be optimized, and the solution performance of the new method is superior to that of the general method.