We consider the general case of a network of
detectors. Let
be the signal vector and let
n
be the noise vector of the network of detectors, i.e., the
vector component
is the response of the gravitational-wave signal in the
th detector with noise
. Let us also assume that each
has zero mean. Assuming that the noise in all detectors is
additive the data vector
can be written as
A derivation of the likelihood function for an
arbitrary network of detectors can be found in
[33], and applications of optimal filtering for the special cases of
observations of coalescing binaries by networks of ground-based
detectors are given in
[39, 27, 66]
and for the case of stellar mass binaries observed by LISA
space-borne detector in
[50]
. A least square fit solution for the estimation of the sky
location of a source of gravitational waves by a network of
detectors for the case of a broad band burst was obtained
in
[36]
.
There is also another important method for analyzing the data from a network of detectors - the search for coincidences of events among detectors. This analysis is particularly important when we search for supernova bursts the waveforms of which are not very well known. Such signals can be easily mimicked by non-Gaussian behavior of the detector noise. The idea is to filter the data optimally in each of the detector and obtain candidate events. Then one compares parameters of candidate events, like for example times of arrivals of the bursts, among the detectors in the network. This method is widely used in the search for supernovae by networks of bar detectors [11] .
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