(in $\alpha$ and $\delta$) from [*Tycho*]{} should in principle suffice to determine the five astrometric parameters. The scans are not purely one-dimensional, but contain some across-scan information (Sect. \[sec:sim\]), which is crucial for the determination of the satellite’s attitude and calibration parameters.

The real data are affected by significant dead time, increasing the time needed for sufficient sky coverage (Sect. \[sec:deadtime\]). Considering that another half year of scanning in principle adds full redundancy to the whole sky, we estimate that the actual amount of [*Gaia*]{} data required for TGAS corresponds to between 0.5 and 1.0 yr including dead time.

Incorporating the [*Tycho*]{} and [Hipparcos]{} information {#sec:priorconstruction}
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TGAS uses the ‘joint solution’ method described in the HTPM paper . That is, the prior information taken from the [Hipparcos]{} or [*Tycho*]{} Catalogue is cast in the form of normal equations ${\boldsymbol}{N}_\text{pri}{\boldsymbol}{x}={\boldsymbol}{b}_\text{pri}$ for the astrometric parameters represented by the vector ${\boldsymbol}{x}$. These equations are then added to the normal equations ${\boldsymbol}{N}_\text{obs}{\boldsymbol}{x}={\boldsymbol}{b}_\text{obs}$ derived from the [*Gaia*]{} observations before calculating the solution ${\boldsymbol}{\hat{x}}=({\boldsymbol}{N}_\text{pri}+{\boldsymbol}{N}_\text{obs})^{-1}({\boldsymbol}{b}_\text{pri}+{\boldsymbol}{b}_\text{obs})$. The main difference compared with HTPM concerns the setting up of the prior information for the non-[Hipparcos]{} stars in the [*Tycho*]{} Catalogue, which is described below. For the subset of [Hipparcos]{} 