# 4.3.7 Global parameters

Author(s): Sergei Klioner

The astrometric software AGIS can be used to fit arbitrary global parameters, that is, parameters that depend on all or most of the data. A flexible software package in AGIS allows one to fit such parameters in different groups and modes. The primary use of this block is the determination of physical parameters, like the PPN parameter $\gamma $. This requires possibly good calibrations and clear understanding of systematic errors. This will be done in the future data releases. Another application of the global block is to determine instrumental (calibration) parameters characterizing Gaia astrometric instrument as a whole. Examples here are the Velocity and Basic Angle Calibration (VBAC) and Focal Length and Optical Distortion Calibration (FOC). VBAC is intended to determine, to the largest possible extent, effective basic angle variations directly from the astrometric data (see also Section 4.2.3). FOC determines arbitrary differential distortions of the Gaia astrometric instrument. In Gaia EDR3, VBAC and FOC were used in the astrometric solution to calibrate variations of the basic angle and differential variations of the astrometric instrument. In this way the influence of both effects on the astrometric solution is mitigated. For Gaia EDR3 a more sophisticated versions of VBAC and FOC compared to the previous data releases were used.

VBAC was fitted as a Fourier polynomial of the heliotropic phase $\mathrm{\Omega}$ of Gaia satellite with the coefficients as linear functions of time multiplied by a factor inversely proportional to the squared helicentric distance of Gaia. In contrast to the previous data release the VBAC model also includes the term proportional to $\mathrm{cos}\mathrm{\Omega}$ that is known to be highly degenerate with the mean parallax zero point (Butkevich et al. 2017). Special care has been taken when fitting this term successfully and this allowed to improve the mean parallax zero point of Gaia EDR3 by about 20 $\mu $as (Lindegren et al. 2021).

FOC was fitted partly as free B-splines of TCB with knot intervals of 20 min (for the distortions depending on the position in the fields of view as Legendre polynomials of orders 1 and 2) and as Fourier polynomials of the heliotropic phase $\mathrm{\Omega}$ of Gaia satellite (for the distortions of order 3). This combination turned out to provide best results for the data of Gaia EDR3. FOC was fitted separately for each field of view.

Both VBAC and FOC were fitted separately for each window class (this effectively allows for a certain magnitude-dependence of the distortions). For the $\mathrm{cos}\mathrm{\Omega}$ effect in VBAC all reasonable data was used to improved the signal-to-noise ratio for the coefficient which was found to be advantageous given the near-degeneracy condition of the fit. Further details of the VBAC and FOC models in Gaia EDR3 can be found in (Lindegren et al. 2021).

Even more sophisticated models for VBAC and FOC should be expected for the future releases.