  The Gaia mission has been designed to perform absolute astrometric
measurements with unprecedented accuracy; the end-of-mission parallax standard
error is required to be 30 micro-arcseconds for a G2V type star of magnitude
15. These requirements set a stringent constraint on the accuracy of the
estimation of the location of the stellar image on the CCD for each
observation: e.g., 0.3 milli-arseconds (mas) or 0.005 pixels for the same V=15
G2V star. However the Gaia CCDs will suffer from charge transfer inefficiency
(CTI) caused by radiation damage that will degrade the stellar image quality
and may degrade the astrometric performance of Gaia if not properly addressed.
For the first time at this level of detail, the potential impact of radiation
damage on the performance of Gaia is investigated. In this first paper we focus
on the evaluation of the CTI impact on the image location accuracy. We show
that CTI decreases the stellar image signal-to-noise ratio and irreversibly
degrades the image location estimation precision. As a consequence the location
estimation standard errors increase by up to 6% for a radiation damage level
equivalent to the end-of-mission. In addition the CTI-induced image distortion
introduces a systematic bias in the image location estimation (up to 0.05
pixels or 3 mas in the Gaia operating conditions). We present a novel approach
to CTI mitigation that enables, without correction of the raw data, the
unbiased estimation of the image location and flux from damaged observations.
Its implementation reduces the maximum measured location bias for the faintest
magnitude to 0.005 pixels (~4e-4 pixels at magnitude 15). In a second paper we
will investigate how the CTI effects affect the final astrometric accuracy of
Gaia by propagating residual errors through the astrometric solution.
