  A data-analysis strategy based on the maximum-likelihood method (MLM) is
presented for the detection of gravitational waves from inspiraling compact
binaries with a network of laser-interferometric detectors having arbitrary
orientations and arbitrary locations around the globe. The MLM is based on the
network likelihood ratio (LR), which is a function of eight signal-parameters
that determine the Newtonian inspiral waveform. In the MLM-based strategy, the
LR must be maximized over all of these parameters. Here, we show that it is
possible to maximize it analytically over four of the eight parameters.
Maximization over a fifth parameter, the time of arrival, is handled most
efficiently by using the Fast-Fourier-Transform algorithm. This allows us to
scan the parameter space continuously over these five parameters and also cuts
down substantially on the computational costs. Maximization of the LR over the
remaining three parameters is handled numerically. This includes the
construction of a bank of templates on this reduced parameter space. After
obtaining the network statistic, we first discuss `idealized' networks with all
the detectors having a common noise curve for simplicity. Such an exercise
nevertheless yields useful estimates about computational costs, and also tests
the formalism developed here. We then consider realistic cases of networks
comprising of the LIGO and VIRGO detectors: These include two-detector
networks, which pair up the two LIGOs or VIRGO with one of the LIGOs, and the
three-detector network that includes VIRGO and both the LIGOs. For these
networks we present the computational speed requirements, network
sensitivities, and source-direction resolutions.
