Abstract
We describe a general mathematical framework for discriminators in the context of the compact binary coalescence (CBC) search. We show that with any is associated a vector bundle over the signal manifold, that is, the manifold traced out by the signal waveforms in the function space of data segments. The is then defined as the square of the norm of the data vector projected onto a finite-dimensional subspace (the fibre) of the Hilbert space of data trains and orthogonal to the signal waveform. Any such fibre leads to a discriminator, and the full vector bundle comprising the subspaces and the base manifold constitute the discriminator. We show that the discriminators used so far in the CBC searches correspond to different fibre structures constituting different vector bundles on the same base manifold, namely, the parameter space. Several benefits accrue from this general formulation. It most importantly shows that there are a plethora of ’s available and further gives useful insights into the vetoing procedure. It indicates procedures to formulate new ’s that could be more effective in discriminating against commonly occurring glitches in the data. It also shows that no with a reasonable number of degrees of freedom is foolproof. It could also shed light on understanding why the traditional works so well. We show how to construct a generic given an arbitrary set of vectors in the function space of data segments. These vectors could be chosen such that glitches have maximum projection on them. Further, for glitches that can be modeled, we are able to quantify the efficiency of a given discriminator by a probability. Second, we propose a family of ambiguity discriminators that is an alternative to the traditional one [B. Allen, Phys. Rev. D 71, 062001 (2005), B. Allen et al., Phys. Rev. D 85, 122006 (2012).]. Any such ambiguity makes use of the filtered output of the template bank, thus adding negligible cost to the overall search. It is termed so because it makes significant use of the ambiguity function. We first describe the formulation with the help of the Newtonian waveform, apply the ambiguity to the spinless TaylorF2 waveforms, and test it on simulated data. We show that the ambiguity essentially gives a clean separation between glitches and signals. We indicate how the ambiguity can be generalized to detector networks for coherent observations. The effects of mismatch between signal and templates on a discriminator using general arguments and the geometrical framework are also investigated.
- Received 11 August 2017
DOI:https://doi.org/10.1103/PhysRevD.96.103018
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