Detection of gravitational waves using a network of detectors

We formulate the data analysis problem for the detection of the Newtonian c oalescing-binary signal by a network of laser interferometric gravitational wave detectors that have arbitrary orientations, but are located at the sa me site. We use the maximum likelihood method for optimizing the detection problem. We show that for networks comprising of up to three detectors, the optimal statistic is just the matched network-filter. Alternatively, it is simply a linear combination of the signal-to-noise ratios of the individua l detectors. This statistic, therefore, can be interpreted as the signal-to -noise ratio of the network. The overall sensitivity of the network is show n to increase roughly as the square-root of the number of detectors in the network. We further show that these results continue to hold even for the r estricted post-Newtonian filters. Finally, our formalism is general enough to be extended, in a straightforward way, to address the problem of detecti on of such waves from other sources by some other types of detectors, eg., bars or spheres, or even by networks of spatially well-separated detectors.