Rigorous Transformation of GPS-determined Vector Components

When GPS-determined vector components are compared or integrated into simultaneous network adjustments, one must be certain that the components of the vectors are rigorously referred to the same epoch and station reference point. This paper gives rigorous matrix transformations to achieve this aim, including changes in coordinate systems, displacements due to plate tectonics, and possible centering and height measuring errors. These transformations are critical to infer accurate geodetic coordinates or when crustal motions or deformation studies are investigated. A practical case involving the shifting of Global Positioning System (GPS) observables from the L1 phase center to the antenna reference point (ARP) was investigated.