2021ApJ...920...43X

Locating gamma-ray transients including gamma-ray bursts (GRBs) and soft gamma repeater (SGR) bursts is of great importance in multi-messenger and multi-wavelength astronomy, such as guiding optical and radio follow-up observations and evaluating the association of a GRB with a gravitational wave or an SGR with a galaxy or fast radio burst (FRB). A time delay (or triangulation) method with multiple missions has been utilized to localize GRBs since their discovery in the 1970s. In this paper, we propose to use the Modified Cross-correlation Function (called Li-CCF hereafter) to derive the accurate time delay from the high time resolution light curves recorded by GRB detectors. This method has been extensively verified with simulation and a sample of GRBs and SGRs with precise positions, using event-by-event data (TTE or Evt data) of Insight-HXMT/HE, Fermi/GBM, Swift/BAT, and GECAM. We find that the 1σ uncertainty (annulus half-width) can be less than 0.3 degrees despite the relatively short distance between these satellites. We note that the localization error given by Li-CCF can be reduced by several times compared with the traditional CCF method or the Fermi/GBM-alone localization, depending on the timing, spectral lag and direction of the GRB, and the distance and number of satellites used. Finally, systematic errors of this time delay method, including the effect of GRB spectral lags and background variation in light curves, have been studied in detail and several improvements have been proposed to deal with those effects.