A Conical Model Approach for Invariant Points of Very Long Baseline Interferometry and Satellite Laser Ranging

Abstract

A new realization of the international terrestrial reference frame, a combination of four different space geodetic techniques, was released in 2022. Each geodetic solution should be combined carefully based on the local tie information at the co-located site. Although many approaches have been successfully applied to connect different geodetic sensors, to date, there has been no unified mathematical representation for the target motions. Herein, a unified conical model was developed to estimate the invariant points of geodetic sensors using a more robust and consistent approach. It modeled the motion of targets, in either the horizontal or vertical axis, as cones; thus, homogeneous modeling was implemented. In addition to its simplicity, the model simultaneously estimated the tilting of the vertical axis and horizontal offset. The mathematical relationship and normality of the normal vector were modeled as a Gauss–Markov model with fixed constraints. The pre-computed initial coordinates of the pillars and targets were adjusted simultaneously to calculate the correlation information for the local tie vector. The complete model was successfully applied to the co-located site, which was transformed into a global reference frame via the Helmert transformation based on the global navigation satellite system campaign. The results showed that the proposed method is more efficient in terms of the number of parameters for invariant points of geodetic sensors (only 13% compared to the 3D circle fitting type conventional approach). In addition, the reliability of the estimated solution can be increased by avoiding an ill-conditioned linear system through the conical model.