Updates to the Fermi GBM Targeted Sub-threshold Search in Preparation for the Third Observing Run of LIGO/Virgo

In this document, we detail the improvements made to the Fermi GBM targeted sub-threshold search for counterparts to LIGO/Virgo gravitational-wave triggers. We describe the implemented changes and compare the sensitivity of the O3 search to that of the version of the search that operated during O2. Overall, we have improved both the sensitivity and speed of the targeted search. Further improvements to the search have been made for the O3b observing run, including automated upperlimits estimation and incorporating the updated localization systematic with the new version of the search.
Comment: Updates and improvements for operations during LIGO/Virgo O3b. New sections on upper limits calculation, localization systematic uncertainty in the search, and a case study on the sub-threshold candidate during O3a: Fermi GBM-190816