@article{3ca32345579e4364b0f17ea69902c227,

title = "Optimal combination of signals from colocated gravitational wave interferometers for use in searches for a stochastic background",

abstract = "This article derives an optimal (i.e., unbiased, minimum variance) estimator for the pseudodetector strain for a pair of colocated 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 Hanford 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 pseudodetector. 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 an {"}off-source{"} measurement to test algorithms used in the {"}on-source{"} observation.",

author = "Albert Lazzarini and Sukanta Bose and Peter Fritschel and Martin McHugh and Tania Regimbau and Kaice Reilly and Romano, {Joseph D.} and Whelan, {John T.} and Stan Whitcomb and Whiting, {Bernard F.}",

note = "Funding Information: One of the authors (A. L.) wishes to thank Sanjeev Dhurandhar for his hospitality at IUCAA during which the paper was completed. He provided helpful insights by pointing out the geometrical nature of the signals and their inherent three-dimensional properties that span the space . This led to an understanding of how diagonalization of the covariance matrix could be achieved only after properly removing the signature of from the interferometer signals. The authors gratefully acknowledge the careful review and helpful suggestions provided by Nelson Christensen which helped finalize ?>the manuscript. This work was performed under partial funding from the following NSF Grants: PHY-0107417, 0140369, 0239735, 0244902, 0300609, and INT-0138459. J. D. R. and T. R. acknowledge partial support on PPARC Grant No. PPA/G/O/2001/00485. This document has ?>been assigned LIGO Laboratory Document No. LIGO-P040006-05-Z.",

year = "2004",

month = sep,

doi = "10.1103/PhysRevD.70.062001",

language = "English",

volume = "70",

pages = "062001--1--062001--12",

journal = "Physical Review D",

issn = "0556-2821",

number = "6",

}