Time-variant transformations for modern terrestrial reference frames.

摘要

Terrestrial reference frames have been playing an important role in engineering applications as well as in scientific research. They provide a conventional definition for most positioning applications. Nowadays modern geodetic techniques, such as Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), and Global Positioning System (GPS) provide accurate positional measurements across the earth and validate a precise definition of modern geodetic datums. The highly-accurate definition of a terrestrial reference frame monitored by continuous/repeated measurements enables one to look at another important issue---the time-dependent variation of terrestrial reference frames. It is a consequence resulting from the Earth's dynamic activities. Modern terrestrial reference frames that exhibit time-variant behavior have been established in recent years at global and continental scales. This work focuses on the study of rigorous transformations between precisely defined time-variant reference frames. Time-variant models particularized to similarity and affine transformations will be established to represent the changing geometrical relationships between different terrestrial reference frames. The indirect problem (i.e. given initial and final coordinates, determine the transformation parameters) corresponding to the models here developed will also be investigated after deriving rigorous solutions based on a step-wise approach. This novel formulation, utilizing intrinsic constraints (i.e. the relationships imbedded in the model), will be advanced to resolve the rank-deficiency problem encountered in time-variant transformation models. It will be shown that the proposed methodology gives realistic solutions to the indirect problem with fewer prerequisites compared to other solutions currently in use. The statistical models will also be addressed so that the quality of a time-variant transformation can be assessed. In particular, an analytical expression for principal component covariance propagation has been developed to enable realistic uncertainty estimations for general affine transformations. All proposed models have been validated using numerical examples invoking real or simulated data. Practical considerations are discussed assessing the pros and cons of the proposed. Applications in the related fields, including a time-variant strain tensor analysis and combination of multiple terrestrial solutions, have been introduced to reveal the added potential of this research.