A Kullback-Leibler-Based Detector Consistency Statistic for Classifying Astrophysical Signals and Detector Artifacts in the Einstein Telescope

Future third-generation gravitational-wave detectors such as the Einstein Telescope (ET) are expected to observe compact binary coalescences at high event rates, which makes the reliable identification of detector artifacts a routine requirement in data analysis rather than an occasional task. We address this by defining a detector-consistency statistic directly in parameter space, constructed from the Kullback–Leibler (KL) divergence between covariance matrices obtained independently for the three ET interferometers. The underlying idea is simple: if a signal is astrophysical and coherent, independent analyses of different detectors tend to produce similar uncertainty structures, whereas incoherent events lead to mismatched covariance estimates. To examine this behaviour in a controlled setting, we apply the method to simulated binary black hole (BBH) and binary neutron star (BNS) populations, together with glitch-like events generated independently in each detector. The results show that astrophysical signals occupy a region of relatively small KL values, while the incoherent population extends to much larger values. When reduced to summary statistics across the three detector pairs, the overlap between the two populations remains limited. The separation can also be quantified through receiver operating characteristic analysis, for which all three KL-based summary statistics give AUC values equal to 1.0000 for both BBH and BNS samples in the present simulation setup. In the same simulations, the KL divergence decreases systematically as the pairwise SNR increases, which is consistent with the expectation that signals at larger pairwise SNR are more tightly constrained and therefore more consistent across detectors. It should be noted, however, that the glitch-like events considered here are constructed as controlled incoherent injections rather than realistic instrumental glitches, so the present results should be interpreted as a proof-of-principle demonstration of detector-consistency discrimination. Since the construction relies only on parameter-estimation outputs rather than directly on strain data, it can be incorporated into existing analysis pipelines without substantial additional cost. The KL-based statistic therefore serves as a practical measure of detector consistency and provides a simple criterion for identifying incoherent events in gravitational-wave observations.