Fusion Model for Long-Term Solutions to the Terrestrial Reference Frame Using Internal Constraints

  Objectives  A terrestrial reference system (TRS) is a spatial reference system corotating with the Earth in its diurnal motion in space. A terrestrial reference frame (TRF) is defined as the realization of a TRS, through the realization of its origin, orientation axes and scale, and their time evolution. The TRF is the basis of all surveying and mapping activities and earth science research. Usually, its realization is achieved by a set of physical points with precisely determined coordinates in a specific coordinate system.

  Methods  The instantaneous positions obtained from different epoch observations are with respect to differ‍ent reference frames. It is necessary to accumulate the instantaneous positions to form a stable long-term reference frame. Taking the instantaneous positions obtained from different epoch observations as input, a fusion model for the long-term solutions to a TRF is designed. The function model for the long-term solutions is deduced in detail considering the coordinate transformation model and the time-varying model of station coordinates. The rank deficiency is solved by applying internal constraints to the Helmert transformation parameters.

  Results  The daily solutions spanning from 2010-08-2014-12 from the sec‍ond reprocessing of International Global Navigation Satellite System Service are used for calculation, and the results are compared with that of the international terrestrial reference frame 2014 (ITRF2014). The results show that for daily solutions the standard deviation is 3.45 mm, 4.04 mm, and 2.84 mm for X, Y and Z directions, respectively, and the weighted root mean square is better than 3 mm for all three directions. In terms of velocity, the accuracy is 1.53 mm/a, 1.46 mm/a, and 1.21 mm/a for X, Y and Z directions, respectively.

  Conclusions   The derived TRF using the fusion model is consistent with ITRF2014, and the results validate the correctness and reliability of our fusion model, which can provide a theoretical basis for the establishment of the reference frame.