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Authors: M. Rakhmanov

Date: Mon, 3 Apr 2006

Abstract: Coherent searches for gravitational-wave bursts rely on methods which combine data from several detectors taking into account differences in their responses. The efforts are now focused on the maximum likelihood principle as the most natural way to combine data, which can also be used without prior knowledge of the signal. Recent studies however have shown that straightforward application of the maximum likelihood method to gravitational waves with unknown waveforms can lead to inconsistencies and unphysical results, such as the discontinuity in the functional form of residual or the divergence of the variance of the estimated solution for some locations in the sky. Several solutions to these problems based on different physical arguments have been proposed so far. In this paper we continue these investigations and show from a very general point of view that the detection of gravitational-wave bursts with a network of detectors belongs to the category of ill-posed problems, i.e. discrete inverse problem with rank-deficient matrix. We describe how to apply Tikhonov regularization technique to resolve the rank deficiency. A variant of Tikhonov regulator which minimizes the condition number of the matrix for all locations in the sky is introduced and its application for burst searches is briefly discussed.

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