  The number of gravitational wave signals from the merger of compact binary
systems detected in the network of advanced LIGO and Virgo detectors is
expected to increase considerably in the upcoming science runs. Once a
confident detection is made, it is crucial to reconstruct the source's
properties rapidly, particularly the sky position and chirp mass, to follow up
on these transient sources with telescopes operating at different
electromagnetic bands for multi-messenger astronomy. In this context, we
present a rapid parameter estimation (PE) method aided by mesh-free
approximations to accurately reconstruct properties of compact binary sources
from data gathered by a network of gravitational wave detectors. This approach
builds upon our previous algorithm [L. Pathak et al., Fast likelihood
evaluation using meshfree approximations for reconstructing compact binary
sources, https://journals.aps.org/prd/abstract/10.1103/PhysRevD.108.064055,
Phys. Rev. D 108, 064055 (2023)] to expedite the evaluation of the likelihood
function and extend it to enable coherent network PE in a ten-dimensional
parameter space, including sky position and polarization angle. Additionally,
we propose an optimized interpolation node placement strategy during the
start-up stage to enhance the accuracy of the marginalized posterior
distributions. With this updated method, we can estimate the properties of
binary neutron star (BNS) sources in approximately 2.4~(2.7) min for the
\TaylorF~(\texttt{IMRPhenomD}) signal model by utilizing 64 CPU cores on a
shared memory architecture. Furthermore, our approach can be integrated into
existing parameter estimation pipelines, providing a valuable tool for the
broader scientific community. We also highlight some areas for improvements to
this algorithm in the future, which includes overcoming the limitations due to
narrow prior bounds.
