  We report the results of a near-infrared survey for long-period variables in
a field of view of 20 arcmin by 30 arcmin towards the Galactic Centre (GC). We
have detected 1364 variables, of which 348 are identified with those reported
in Glass et al. (2001). We present a catalogue and photometric measurements for
the detected variables and discuss their nature. We also establish a method for
the simultaneous estimation of distances and extinctions using the
period-luminosity relations for the JHKs bands. Our method is applicable to
Miras with periods in the range 100--350 d and mean magnitudes available in two
or more filter bands. While J-band means are often unavailable for our objects
because of the large extinction, we estimated distances and extinctions for 143
Miras whose H- and Ks-band mean magnitudes are obtained. We find that most are
located at the same distance to within our accuracy. Assuming that the
barycentre of these Miras corresponds to the GC, we estimate its distance
modulus to be 14.58+-0.02(stat.)+-0.11(syst.) mag, corresponding to
8.24+-0.08(stat.)+-0.42(syst.) kpc. We have assumed the distance modulus to the
LMC to be 18.45 mag, and the uncertainty in this quantity is included in the
systematic error above. We also discuss the large and highly variable
extinction. Its value ranges from 1.5 mag to larger than 4 mag in A(Ks) except
towards the thicker dark nebulae and it varies in a complicated way with the
line of sight. We have identified mid-infrared counterparts in the Spitzer/IRAC
catalogue of Ramirez et al. (2008) for most of our variables and find that they
follow rather narrow period-luminosity relations in the 3.6 to 8.0 micrometre
wavelength range.
