Establishing Global Reference Frames. Nonlinear, Temporal, Geophysical and Stochastic Aspects

The problem of the optimal definition of a Global Reference Frame based on a geodetic network of continuously observing stations is analyzed from various points of view. The non-linear datum definition problem is extended to the time domain and the optimal reference frame for a de-formable network is obtained as a geodesic line on a curved manifold in the vector space of all network coordinates, which is the union of instantaneous shape manifolds. The original ideas of Meissl are extended from the linear to the non-linear case and from the space to the space-time domain. The resulting definition of a Meissl Reference Frame is shown to be a geodesic frame as well as a Tisser-and-type frame. The difference between the operational Meissl-Tisserand geodetic network frame and the theoretical geophysical Tisserand earth frame is emphasized and it is shown how a connection between the two can be established by incorporating geophysical hypotheses, such as plate tectonics. Finally the stochastic problem of the optimal combination of estimated network frames is examined from both a non-linear and an approximate linearized solution point of view.