Prompt sky localization of compact binary sources using mesh free approximation

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 (Pathak et al.\cite{pathak2022rapid}) 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) minutes 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.