Application of Time Transfer Functions to Gaia's global astrometry -
  Validation on DPAC simulated Gaia-like observations
  A key objective of the ESA Gaia satellite is the realization of a
quasi-inertial reference frame at visual wavelengths by means of global
astrometric techniques. This requires an accurate mathematical and numerical
modeling of relativistic light propagation, as well as double-blind-like
procedures for the internal validation of the results, before they are released
to the scientific community at large. Aim of this work is to specialize the
Time Transfer Functions (TTF) formalism to the case of the Gaia observer and
prove its applicability to the task of Global Sphere Reconstruction (GSR), in
anticipation of its inclusion in the GSR system, already featuring the suite of
RAMOD models, as an additional semi-external validation of the forthcoming Gaia
baseline astrometric solutions. We extend the current GSR framework and
software infrastructure (GSR2) to include TTF relativistic observation
equations compatible with Gaia's operations. We use simulated data generated by
the Gaia Data Reduction and Analysis Consortium (DPAC) to obtain different
least-squares estimations of the full stellar spheres and gauge results. These
are compared to analogous solutions obtained with the current RAMOD model in
GSR2 and to the catalog generated with GREM, the model baselined for Gaia and
used to generate the DPAC synthetic data. Linearized least-squares TTF
solutions are based on spheres of about 132,000 primary stars uniformly
distributed on the sky and simulated observations spanning the entire 5-yr
range of Gaia's nominal operational lifetime. The statistical properties of the
results compare well with those of GREM. Finally, comparisons to RAMOD@GSR2
solutions confirmed the known lower accuracy of that model and allowed us to
establish firm limits on the quality of the linearization point outside of
which an iteration for non-linearity is required for its proper convergence.
