Biases depending on PSF distortions due to the SSO sources could not be corrected in Gaia DR2. The adopted
strategy consisted in rejecting the centroids (and corresponding fluxes) that, within a given probability, could have been affected
by a bias larger than the random error due to the photons noise statistics. The aim of this procedure was to avoid, as much as possible,
the use of centroids likely affected by some non negligible systematic biases in the following astrometric reduction processing.

A large set of numerical simulations were performed in order to evaluate the expected
centroid and flux bias affecting IPD in a variety of possible situations.
In the simulations, nominal PSFs for Solar-type sources were
used to model the ${\varphi}_{s}$ function (for the meaning of the ${\varphi}_{s}$, ${\mathrm{\Phi}}_{s}$, $\mathrm{\Delta}{x}_{s}$ and $\mathrm{\Delta}{f}_{s}$
symbols used in this paragraph, see Section 4.4.2).
Values of resulting $\mathrm{\Delta}{x}_{s}$ and $\mathrm{\Delta}{f}_{s}$ were computed for different
values of the relevant parameters, namely the window size, the centroid position and the source velocity.
Figure 4.20
shows an example of this exercise. Two plots of $\mathrm{\Delta}{x}_{s}/{\sigma}_{x}$ versus the
centroid position are shown, where ${\sigma}_{x}$ is the uncertainty in the centroid determination
mainly due to photon
statistics, which in turn depends on the source magnitude. Two cases for magnitude $12$ and $18$ are shown.
It is possible to see how the interval $[-{\mathcal{R}}_{x},+{\mathcal{R}}_{x}]$ of centroid coordinates (with respect to the window centre)
for which $$ depends on
source apparent velocity and magnitude. The larger the velocity, the more ${\mathrm{\Phi}}_{s}$ differs from ${\varphi}_{s}$ and the larger is
the bias, while the interval $[-{\mathcal{R}}_{x},+{\mathcal{R}}_{x}]$ tends to shrink around zero (${\mathcal{R}}_{x}$ decreases). The fainter is the magnitude, the larger
the centroiding error ${\sigma}_{x}$, therefore the condition $$ corresponds to wider
intervals $[-{\mathcal{R}}_{x},+{\mathcal{R}}_{x}]$ (${\mathcal{R}}_{x}$ increases).

The value ${\mathcal{R}}_{x}$ is a function of the instrument PSF ${\varphi}_{s}$,
the number of along-scan samples ${N}_{x}$, the binning ${B}_{x}$ (number of pixels per samples), the magnitude of the source $M$ and its along-scan velocity ${v}_{x}$.
The function ${\varphi}_{s}$ is not exactly known but it can be approximated on the basis of numerical simulations and nominal payload design. The same for the
motion ${v}_{x}$, that it is estimated by the IDT/IDU system or it can be constrained by introducing some *a priori* limits
(for example, about $90$% of the Main Belt Asteroids are expected
to show an along-scan motion less than $20$ mas/s). The value of the magnitude was estimated on-board by the VPU.
In conclusion, from a statistical point of view, we can estimate, for each transit and window, the value ${\mathcal{R}}_{x}$ such that
if ${x}_{s}\notin [-{\mathcal{R}}_{x},+{\mathcal{R}}_{x}]$. In such cases, most likely ${x}_{s}$ is affected by a bias $\mathrm{\Delta}{x}_{s}$ larger than its random error due to the photon noise.
Whenever this happened, the centroid value ${x}_{s}$ was rejected, and the corresponding CCD strip removed from the data processing pipeline.