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A vitally important requirement for detecting gravitational wave (GW) signalsfrom compact coalescing binaries (CBC) with high significance is the reductionof the false-alarm rate of the matched-filter statistic. The data from GWdetectors contain transient noise artifacts, or glitches, which adverselyaffect the performance of search algorithms by producing false alarms. Glitcheswith large amplitudes can produce triggers in the SNR time-series in spite oftheir small overlap with the templates. This contributes to false alarms.Historically, the traditional $\chi^2$ test has proved quite useful indistinguishing triggers arising from CBC signals and those caused by glitches.In a recent paper, a large class of unified $\chi^2$ discriminators wasformulated, along with a procedure to construct an optimal $\chi^2$discriminator, especially, when the glitches can be modeled. A large variety ofglitches that often occur in GW detector data can be modeled as sine-Gaussians,with quality factor and central frequency, ($Q,f_0$), as parameters. We useSingular Value Decomposition to identify the most significant degrees offreedom in order to reduce the computational cost of our $\chi^2$. Finally, weconstruct a $\chi^2$ statistic that optimally discriminates betweensine-Gaussian glitches and CBC signals. We also useReceiver-Operating-Characteristics to quantify the improvement in searchsensitivity when it employs the optimal $\chi^2$ compared to the traditional$\chi^2$. The improvement in detection probability is by a few to severalpercentage points, near a false-alarm probability of a few times $10^{-3}$, andholds for binary black holes (BBHs) with component masses from several to ahundred solar masses. Moreover, the glitches that are best discriminatedagainst are those that are like sine-Gaussians with $Q\in [25,50]$ and $f_0\in[40,80]$Hz.

An optimal $\chi^2$ discriminator against modelled noise-transients in interferometric data in searches for binary black-hole mergers