Constructing an optimal chi-square discriminator for modeled glitches in interferometric data

Abstract

The interferometric data from gravitational wave detectors is neither Gaussian nor stationary and contains noise transients or glitches. These glitches interfere with the search algorithms by producing high SNR triggers. In particular, for the compact coalescing binary search which is carried out by a bank of templates, the glitches in spite of their small overlap with the templates, because of their high amplitude, can produce detectable triggers thus giving false alarms. Usually, the Allen chi-square test is then used to distinguish between the signal and the glitch. In a recent paper [1], a uni ed description of all possible chi-square discriminators is given, and also a constructive procedure is described to construct an optimal chi-square discriminator especially if the glitch can be modeled. One such type of glitch that often occurs in the data can be modeled as a sine-Gaussian with parameters (Q; f0). An important property of sine-Gaussian glitch is that there is a time-lag between the trigger and the occurrence of the glitch. Therefore the time-lag is considered separately and we construct the parameter space using uniformly distributed points on it. The total number of points on the parameter space is associated with the degrees of freedom (d.o.f) of the chi-square. To reduce the d.o.f, we describe a method which uses Singular Value Decomposition that helps us to reduce and nd the optimal number of d.o.f for the chi-square. Finally, we present a way to construct an optimal chi-square discriminator for sine-Gaussian glitches using the procedure in the paper