Composite gravitational-wave detection of compact binary coalescence

The detection of gravitational waves from compact binaries relies on a computationally burdensome processing of gravitational-wave detector data. The parameter space of compact-binary-coalescence gravitational waves is large and optimal detection strategies often require nearly redundant calculations. Previously, it has been shown that singular value decomposition of search filters removes redundancy. Here we will demonstrate the use of singular value decomposition for a composite detection statistic. This can greatly improve the prospects for a computationally feasible rapid detection scheme across a large compact binary parameter space.

Figure 1

The coefficients $w_k$ used to construct the composite detection statistic as a function of basis vector number, ordered by their singular value. The solid-line trace shows the coefficients we obtain from (19), assuming a signal amplitude $A=20$. The dashed-line trace shows the singular values squared, the choice of coefficients given in (11). The dotted-line trace shows “the excess power” choice of coefficients, which is unity for all basis vectors.

Figure 2

Detection probability at a false alarm probability of ${10}^{-3}$ as a function of $A$. We simulated $\sim 1.8\times {10}^7$ signals at SNR 7 for 300 values of $A$ in the composite detection statistic defined by (21). As we expect, the detection probability peaks when $A=7$, the amplitude of the signal. It is worth noting that in this case the low amplitude limit given by (22a) provides a similar detection probability. However, the large signal limit given by (22b) is considerably worse.

Figure 3

Receiver operator characteristic curves associated with different detection statistics. The solid-line trace shows the performance of choosing the maximum likelihood filter across the bank. The dashed-line trace shows the performance of the composite detection statistic. The dotted-line trace shows the performance of choosing the maximum SNR across the bank after conditionally thresholding on the composite detection statistic.