The gamma reaction history diagnostic at the National Ignition Facility has the capability to determine a number of important performance metrics for cryogenic deuterium-tritium implosions: the fusion burn width, bang time and yield, as well as the areal density of the compressed ablator. Extracting those values from the measured γ rays of an implosion, requires accounting for a γ-ray background in addition to the impulse response function of the instrument. To address these complications, we have constructed a model of the γ-ray signal, and are developing a simultaneous multi-shot fitting routine to constrain its parameter space.