The ITRF Beyond the "Linear" Model. Choices and Challenges

The current Solution to the choice of a reference system for the coordinates of a global geodetic network is based on a linear model for the time evolution of station coordinates. The advantages and disadvantages between a mathematical approach and a physical approach to the optimal definition of a reference system for the International Terrestrial Reference Frame (ITRF) are examined. The optimality conditions are derived for a general class of models, consisting of linear combinations of a system of base functions which is closed under differentiation and multiplication. The general results are then applied and elaborated for polynomial and Fourier Series models. Finally the problem of how these conditions should be implemented in practice is investigated.