Constraint Likelihood analysis for a network of gravitational wave detectors

TL;DR

This paper introduces a new constrained likelihood method for detecting and reconstructing gravitational wave signals from a network of interferometric detectors, improving source localization accuracy over standard techniques.

Contribution

The authors develop a novel constrained likelihood approach that addresses limitations of the standard method, applicable to arbitrary detector orientations and capable of source reconstruction.

Findings

Enhanced source coordinate reconstruction accuracy.

Method applicable to any detector network configuration.

Numerical simulations demonstrate improved performance.

Abstract

We propose a coherent method for the detection and reconstruction of gravitational wave signals for a network of interferometric detectors. The method is derived using the likelihood functional for unknown signal waveforms. In the standard approach, the global maximum of the likelihood over the space of waveforms is used as the detection statistic. We identify a problem with this approach. In the case of an aligned pair of detectors, the detection statistic depends on the cross-correlation between the detectors as expected, but this dependence dissappears even for infinitesimally small misalignments. We solve the problem by applying constraints on thelikelihood functional and obtain a new class of statistics. The resulting method can be applied to the data from a network consisting of any number of detectors with arbitrary detector orientations. The method allows us reconstruction of the source coordinates and the waveforms of two polarization components of a gravitational wave. We study the performance of the method with numerical simulation and find the reconstruction of the source coordinates to be more accurate than in the standard approach.