nazgul: A statistical approach to gamma-ray burst localization. Triangulation via non-stationary time-series models. (arXiv:2009.08350v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Burgess_J/0/1/0/all/0/1">J. Michael Burgess</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Cameron_E/0/1/0/all/0/1">Ewan Cameron</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Svinkin_D/0/1/0/all/0/1">Dmitry Svinkin</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Greiner_J/0/1/0/all/0/1">Jochen Greiner</a>
Context. Gamma-ray bursts can be located via arrival time signal
triangulation using gamma-ray detectors in orbit throughout the solar system.
The classical approach based on cross-correlations of binned light curves
ignores the Poisson nature of the time-series data, and is unable to model the
full complexity of the problem.
Aims. To present a statistically proper and robust GRB timing/triangulation
algorithm as a modern update to the original procedures used for the
Interplanetary Network (IPN).
Methods. A hierarchical Bayesian forward model for the unknown temporal
signal evolution is learned via random Fourier features (RFF) and fitted to
each detector’s time-series data with time-differences that correspond to GRB’s
position on the sky via the appropriate Poisson likelihood.
Results. Our novel method can robustly estimate the position of a GRB as
verified via simulations. The uncertainties generated by the method are robust
and in many cases more precise compared to the classical method. Thus, we have
a method that can become a valuable tool for gravitational wave follow-up. All
software and analysis scripts are made publicly available here
(https://github.com/grburgess/nazgul) for the purpose of replication.
Context. Gamma-ray bursts can be located via arrival time signal
triangulation using gamma-ray detectors in orbit throughout the solar system.
The classical approach based on cross-correlations of binned light curves
ignores the Poisson nature of the time-series data, and is unable to model the
full complexity of the problem.
Aims. To present a statistically proper and robust GRB timing/triangulation
algorithm as a modern update to the original procedures used for the
Interplanetary Network (IPN).
Methods. A hierarchical Bayesian forward model for the unknown temporal
signal evolution is learned via random Fourier features (RFF) and fitted to
each detector’s time-series data with time-differences that correspond to GRB’s
position on the sky via the appropriate Poisson likelihood.
Results. Our novel method can robustly estimate the position of a GRB as
verified via simulations. The uncertainties generated by the method are robust
and in many cases more precise compared to the classical method. Thus, we have
a method that can become a valuable tool for gravitational wave follow-up. All
software and analysis scripts are made publicly available here
(https://github.com/grburgess/nazgul) for the purpose of replication.
http://arxiv.org/icons/sfx.gif
