Optimal combination of signals from co-located gravitational wave interferometers for use in searches for a stochastic background

TL;DR

This paper develops an optimal unbiased estimator for co-located gravitational wave detectors, improving stochastic background searches by accounting for instrumental correlations without assumptions on signal strength.

Contribution

It introduces a robust, minimum variance estimator for co-located detectors that handles instrumental correlations and provides a dual measurement for validation.

Findings

Derived an optimal estimator for co-located detectors

Provided an expression for combined noise spectral density

Enabled improved stochastic background detection

Abstract

This article derives an optimal (i.e., unbiased, minimum variance) estimator for the pseudo-detector strain for a pair of co-located gravitational wave interferometers (such as the pair of LIGO interferometers at its Hanford Observatory), allowing for possible instrumental correlations between the two detectors. The technique is robust and does not involve any assumptions or approximations regarding the relative strength of gravitational wave signals in the detector pair with respect to other sources of correlated instrumental or environmental noise. An expression is given for the effective power spectral density of the combined noise in the pseudo-detector. This can then be introduced into the standard optimal Wiener filter used to cross-correlate detector data streams in order to obtain an optimal estimate of the stochastic gravitational wave background. In addition, a dual to the optimal estimate of strain is derived. This dual is constructed to contain no gravitational wave signature and can thus be used as on "off-source" measurement to test algorithms used in the "on-source" observation.