  The infrared Calcium Triplet and its nearby spectral region have been used
for spectral and luminosity classification of late-type stars, but the samples
of cool supergiants (CSGs) used have been very limited (in size, metallicity
range, and spectral types covered). The spectral range of the Gaia Radial
Velocity Spectrograph (RVS) covers most of this region but does not reach the
main TiO bands in this region, whose depths define the M sequence. We study the
behaviour of spectral features around the Calcium Triplet and develop effective
criteria to identify and classify CSGs, comparing their efficiency with other
methods previously proposed. We measure the main spectral features in a large
sample (almost 600) of CSGs from three different galaxies, and we analyse their
behaviour through a principal component analysis. Using the principal
components, we develop an automatised method to differentiate CSGs from other
bright late-type stars, and to classify them. The proposed method identifies a
high fraction of the supergiants (SGs) in our test sample, which cover a wide
metallicity range (SGs from the SMC, the LMC, and the Milky Way) and with
spectral types from G0 up to late-M. In addition, it is capable to separate
most of the non-SGs in the sample, identifying as SGs only a very small
fraction of them. A comparison of this method with other previously proposed
shows that it is more efficient and selects less interlopers. A way to
automatically assign a spectral type to the SGs is also developed. We apply
this study to spectra at the resolution and spectral range of the Gaia RVS,
with a similar success rate. The method developed identifies and classifies
CSGs in large samples, with high efficiency and low contamination, even in
conditions of wide metallicity and spectral-type ranges.
