& 0 & \sigma_{\varpi}^2 & 0 & 0 & 0\\
        0 & 0 & 0 & \sigma_{\mu\alpha*}^2 & 0 & 0\\
        0 & 0 & 0 & 0 & \sigma_{\mu\delta}^2 & 0\\
        0 & 0 & 0 & 0 & 0 & \sigma_{\mu r}^2\\  
        \end{bmatrix} .\end{aligned}$$ The prior information including the covariance is subsequently propagated to the [*Gaia*]{} reference epoch ($\sim$2015) and ${\boldsymbol}{N}_\text{pri}$ is calculated as the inverse of the propagated covariance matrix. ${\boldsymbol}{b}_\text{pri}$ is calculated from the difference between the prior astrometric parameters and the current best estimate in the solution, as described in the HTPM paper, Eq. (18).

Simulations\[sec:sim\]
======================

In order to study the feasibility of TGAS and its potential performance we have made numerical simulations of joint [*Tycho*]{}–[*Gaia*]{} solutions using the AGISLab software package. AGISLab was created at Lund Observatory to develop and test [*Gaia*]{} astrometric data processing strategies. While employing the same solution algorithms as the AGIS software used to process the real [*Gaia*]{} data , it runs in a much simplified framework which also allows us to generate simulated input data (CCD transits). The present experiments are made in a similar manner as described in the HTPM paper, to which we refer for details. 