  We propose a coherent method for the detection and reconstruction of
gravitational wave signals for a network of interferometric detectors. The
method is derived using the likelihood functional for unknown signal waveforms.
In the standard approach, the global maximum of the likelihood over the space
of waveforms is used as the detection statistic. We identify a problem with
this approach. In the case of an aligned pair of detectors, the detection
statistic depends on the cross-correlation between the detectors as expected,
but this dependence dissappears even for infinitesimally small misalignments.
We solve the problem by applying constraints on thelikelihood functional and
obtain a new class of statistics. The resulting method can be applied to the
data from a network consisting of any number of detectors with arbitrary
detector orientations. The method allows us reconstruction of the source
coordinates and the waveforms of two polarization components of a gravitational
wave. We study the performance of the method with numerical simulation and find
the reconstruction of the source coordinates to be more accurate than in the
standard approach.
