nazgul: A statistical approach to gamma-ray burst localization. Triangulation via non-stationary time-series models

TL;DR

This paper introduces a Bayesian statistical method for more accurate gamma-ray burst localization using time-series data, improving upon classical triangulation techniques by modeling the Poisson nature of the data.

Contribution

A novel hierarchical Bayesian approach utilizing random Fourier features for robust and precise GRB localization, updating traditional triangulation methods with a statistically rigorous framework.

Findings

Method accurately estimates GRB positions in simulations.

Uncertainties are more robust and often more precise than classical methods.

Software is publicly available for replication and further use.

Abstract

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.