  Several large-scale gravitational wave (GW) interferometers have achieved
long term operation at design sensitivity. Questions arise on how to best
combine all available data from detectors of different sensitivities for
detection, consistency check or veto, localization and waveform extraction. We
show that these problems can be formulated using the singular value
decomposition (SVD) method. We present techniques based on the SVD method for
(1) detection statistic, (2) stable solutions to waveforms, (3) null-stream
construction for an arbitrary number of detectors, and (4) source localization
for GWs of unknown waveforms.
