8.4.1 Quality control of centroid fitting
Author(s): Aldo Dell’Oro
As far as quality control and rejection at CCD level is concerned, the processing of SSO input data includes three consecutive filtering steps:

1.
preliminary checking of windows;

2.
a control of the IPD quality code;

3.
a filtering of the centroids in order to mitigate the impact of biases described in Section 8.3.2.
Each step is described in detail in the following subsections.
Preliminary windows check
Only centroids and fluxes obtained from windows with standard characteristics were accepted and transmitted to the following steps of the CU4 processing chain. Windows were required to have normal rectangular shape and all samples of the same window had to have the same integration time. Moreover, windows were processed only if possible intrafield conflicts had been fully resolved and did not go through any kind of truncation. By intrafield conflicts, we mean cases in which images coming from the two FOVs of Gaia may receive partly overlapping windows on the focal plane. Finally, windows affected by charge injections were also discarded.
IPD quality control
IDT and IDU output data are provided together with a set of parameters summarizing possible problems encountered during the IPD process and the quality of the final result. In some cases, the centroids and fluxes from IDT and IDU may be included in the database in spite of some anomalies identified during the centroiding process. Typical situations are as follows: (1) the maximum number of allowed iterations in the recursive algorithm of maximization of the adopted likelihood function is exceeded; (2) the detection of some illegal input due to charge injection close to the window; and (3) other particular problems like cosmic rays. In order to avoid such kind of situations, only IDT and IDU centroiding results, for which the relevant quality code indicates a fully successful IPD process, were accepted.
It must be noted, however, that no filtering or rejection was done on the basis of the final goodness of fit of the IPD process. The reason is that the signal of an SSO is not expected to be perfectly described by the pure instrumental PSF used by IDT and IDU, mainly due to the SSO residual motion with respect to the TDI charge transfer. As a consequence, the ${\chi}^{2}$ values may well be often worse than in the case of stellar sources. On the other hand, this fact does not necessarily mean that the values of the centroids and fluxes obtained using only the PSF are completely unreliable, as discussed in what follows.
Bias mitigation
Biases depending on PSF distortions due to the SSO sources could not be corrected in Gaia DR3. The adopted strategy consisted of 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 photon noise statistics. The aim of this procedure was to avoid in the subsequent astrometric processing, as much as possible, the use of centroids likely to be affected by some nonnegligible systematic biases.
A large set of numerical simulations have been performed in order to evaluate the expected centroid and flux bias in IPD in a variety of possible situations. In the simulations, nominal PSFs for solartype 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 8.3.2). Values of $\mathrm{\Delta}{x}_{s}$ and $\mathrm{\Delta}{f}_{s}$ were computed for different values of the relevant parameters, namely the window size, centroid position, and the source motion. Figure 8.16 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 formal uncertainty in the centroid determination mainly due to photon statistics which in turn depend on the source magnitude. The cases are shown for the magnitudes $12$ and $18$. It is possible to see how the interval $[{\mathcal{R}}_{x},+{\mathcal{R}}_{x}]$ of the centroid coordinates (with respect to the window centre), for which $$, depends on source apparent motion and magnitude. The larger the motion, the more ${\mathrm{\Phi}}_{s}$ differs from ${\varphi}_{s}$ and the larger is the bias, whereas the interval $[{\mathcal{R}}_{x},+{\mathcal{R}}_{x}]$ tends to shrink around zero (the positive quantity ${\mathcal{R}}_{x}$ decreases). The fainter the magnitude, the larger is the centroiding error ${\sigma}_{x}$, therefore, the condition $$ corresponds to wider intervals of $[{\mathcal{R}}_{x},+{\mathcal{R}}_{x}]$ (${\mathcal{R}}_{x}$ increases).
The value of ${\mathcal{R}}_{x}$ is a function of the instrument PSF ${\varphi}_{s}$, the number of alongscan samples ${N}_{x}$, the binning ${B}_{x}$ (number of pixels per samples), the alongscan motion ${v}_{x}$ of the source, and its magnitude $M$. The alongscan motion ${v}_{x}$ is estimated by the IDT and IDU systems or it can be constrained by introducing some a priori limits (for example, about $90$ % of the MBAs are expected to show alongscan motion less than $20$ mas s${}^{1}$). The value of the magnitude is estimated as described in Section 8.3.2.
In conclusion, from a statistical point of view, we can estimate the interval $[{\mathcal{R}}_{x},+{\mathcal{R}}_{x}]$ of the centroid values so that their systematic biases are negligible in comparison to their formal random errors. In case it is found outside the interval $[{\mathcal{R}}_{x},+{\mathcal{R}}_{x}]$, the centroid value ${x}_{s}$ is rejected and the corresponding CCD strip is removed from subsequent data processing.