On the application of T-norms to gravitational wave data fusion: A confirmatory study

Abstract

The empirical evidence of gravitational waves (GWs), as they were envisioned by Einstein in his General Theory of Relativity, leads to common questions to be answered in analyzing the observed data. Among them, the need for localizing the cosmological source emitting a gravitational wave. We suggested a Fuzzy Logic approach based on t-norms of time-frequency representations (TFRs) in order to combine data gathered by multiple non-colocated GW detectors. In this paper, we present the results of validating the proposed method with a larger set of TFRs, over both simulated data and public domain LIGO data concerning the eleven GW events identified during the first observing runs of the LIGO-Virgo advanced gravitational wave detector network. Results definitively show the robustness of the proposed approach. In addition, it outperforms the cross-correlation and phase correlation methods, largely used in practice.