The Choice of Reference System in ITRF Formulation

The problem of choosing an optimal reference system for the International Terrestrial Reference Frame (ITRF) is studied for both the rigorous solution which is a simultaneous stacking (removal of the reference system at each data epoch and implementation of a linear in time coordinate model) for all techniques, as well as for the usual numerically convenient separation into a set of individual stackings one for each technique and a final combination step for the derived initial coordinates and velocities. Two approaches are followed, an algebraic and a kinematic one. The algebraic approach implements the inner constraints, which minimize the sum of squares of the unknown parameters, as well as partial inner constraints, which minimize the sum of squares of a subset of the unknown parameters. In the kinematical approach the optimal minimal constraints are derived by requiring the minimization of the apparent coordinate variations: (a) with respect to the origin by imposing constant coordinates for the network barycenter, (b) with respect to orientation by imposing zero relative angular momentum for the network points conceived as mass points with equal mass and (c) with respect to the scale by imposing constant mean quadratic size (involving the distances of stations from their barycenter).