  In a noisy environment with weak single levels, quantum illumination can
outperform classical illumination in determining the presence and range of a
target object even in the limit of sub-optimal measurements based on
non-simultaneous, phase-insensitive coincidence counts. Motivated by realistic
experimental protocols, we present a theoretical framework for analysing
coincident multi-shot data with simple detectors. This approach allows for the
often-overlooked non-coincidence data to be included, as well as providing a
calibration-free threshold for inferring the presence and range of an object,
enabling a fair comparison between different detection regimes. Our results
quantify the advantage of quantum over classical illumination when performing
target discrimination in a noisy thermal environment, including estimating the
number of shots required to detect a target with a given confidence level.
