Abstract:
Even with the best noise canceling techniques, the data in the ground-based gravitational
wave detectors are often plagued with non-stationary noise transients (glitches). These noise
transients severely affect the precision of the matched filtering technique used to detect CBC
signals [8],[6]. Hence, additional statistical tests (discriminators) are required. In 2017, a
unified chi-squared formalism was proposed, which is a mathematical framework for all
single detector chi-squared distributed tests constructed in the context of CBC searches. This formalism, gave a procedure to construct a plethora of chi-squared discriminator tests and also gave a
way to quantify the efficiency of a test at discriminating a certain glitch type. Consequently,
it showed that previously known tests like the Allen’s chi-squared tests are special cases of the
formalism. While the authors of the Unified chi-squared formalism paper also hint at a way to extend the formalism to the coherent multidetector case, they leave this case open for research.
In this thesis, we explore the case of a coherent network of multiple detectors. We interpret
the previously known Null SNR test (Ref. [5]) as a part of the extended unified chi-squared formalism. Consequently, we also construct other Null SNR-like tests which are constructed using subsets of the Null Space, while the Null SNR is constructed using the whole Null Space. In addition to these tests we propose a class of Network chi-squared tests, chi-squared_general (statistically independent from Null SNR-like tests), that are derived from the basis vectors used in the single detector chi-square tests in all the detectors.
The Null SNR like tests can sometimes be weak at discriminating double (multiple) coincident
glitches, while chi-squared_general does not face this issue. Also, unlike Null SNR-like tests, chi-squared_general tests do not exploit the information contained in the detector beam pattern functions.
Hence a network chi-square test which is an addition of a null SNR like test and a chi-squared_general test should address both the weaknesses.
In addition to the theory, we have also numerically tested some of these discriminators.
One such illustration is presented in this thesis.
