nazgul: A statistical approach to gamma-ray burst localization

Triangulation via non stationary time series models

¹ Max-Planck-Institut fur extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching, Germany
e-mail: jburgess@mpe.mpg.de
² Curtin University, Kent Street, Bentley, Perth 6102 WA, Australia
³ Ioffe Institute, 26 Politekhnicheskaya, St Petersburg 194021, Russia

Received: 17 September 2020
Accepted: 15 June 2021

Abstract

Context. Gamma-ray bursts (GRBs) 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 it is unable to model the full complexity of the problem.

Aims. We aim to present a statistically proper and robust GRB timing and triangulation algorithm as a modern update to the original procedures used for the interplanetary network.

Methods. A hierarchical Bayesian forward model for the unknown temporal signal evolution is learned via random Fourier features and fitted to each detector’s time series data with time differences that correspond to the position GRBs 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.