  Rapid parameter estimation of gravitational waves from binary neutron star
coalescence, in particular accurate sky localisation in minutes after the
initial detection stage, is crucial for the success of multi-messenger
observations. One of the techniques to speed up the parameter estimation, which
has been applied for the production analysis of the LIGO-Virgo collaboration,
is reduced order quadrature (ROQ). While it speeds up parameter estimation
significantly, the time required is still on the order of hours. Focusing on
the fact that the parameter-estimation follow-up can be tuned with the
information available at the detection stage, we improve the ROQ technique and
develop a new technique, which we designate focused reduced order quadrature
(FROQ). We find that FROQ speeds up the parameter estimation by a factor of
$\mathcal{O}(10^3)$ to $\mathcal{O}(10^4)$ and enables providing accurate
source properties such as the location of a source in several tens of minutes
after detection.
