Early gravitational-wave data analysis was
concerned with the detection of bursts originating from supernova
explosions
[84]
. It involved analysis of the coincidences among the
detectors
[43]
. With the growing interest in laser interferometric
gravitational-wave detectors that are broadband it was realized
that sources other than supernovae can also be detectable
[79]
and that they can provide a wealth of astrophysical
information
[73, 49]
. For example the analytic form of the gravitational-wave signal
from a binary system is known in terms of a few parameters to a
good approximation. Consequently one can detect such a signal by
correlating the data with the waveform of the signal and
maximizing the correlation with respect to the parameters of the
waveform. Using this method one can pick up a weak signal from
the noise by building a large signal-to-noise ratio over a wide
bandwidth of the detector
[79
]
. This observation has led to a rapid development of the theory
of gravitational-wave data analysis. It became clear that the
detectability of sources is determined by optimal signal-to-noise
ratio, Equation (22
), which is the power spectrum of the signal divided by the power
spectrum of the noise integrated over the bandwidth of the
detector.
An important landmark was a workshop entitled
Gravitational Wave Data Analysis
held in Dyffryn House and Gardens, St. Nicholas near
Cardiff, in July 1987
[74]
. The meeting acquainted physicists interested in analyzing
gravitational-wave data with the basics of the statistical theory
of signal detection and its application to detection of
gravitational-wave sources. As a result of subsequent studies the
Fisher information matrix was introduced to the theory of the
analysis of gravitational-wave data
[32, 48]
. The diagonal elements of the Fisher matrix give lower bounds on
the variances of the estimators of the parameters of the signal
and can be used to assess the quality of astrophysical
information that can be obtained from detections of
gravitational-wave signals
[27
, 47, 15]
. It was also realized that application of matched-filtering to
some sources, notably to continuous sources originating from
neutron stars, will require extraordinary large computing
resources. This gave a further stimulus to the development of
optimal and efficient algorithms and data analysis methods
[75
]
.
A very important development was the work by
Cutler et al.
[26]
where it was realized that for the case of coalescing binaries
matched filtering was sensitive to very small post-Newtonian
effects of the waveform. Thus these effects can be detected. This
leads to a much better verification of Einstein’s theory of
relativity and provides a wealth of astrophysical information
that would make a laser interferometric gravitational-wave
detector a true astronomical observatory complementary to those
utilizing the electromagnetic spectrum. As further developments
of the theory methods were introduced to calculate the quality of
suboptimal filters
[7], to calculate the number of templates to do a search using
matched-filtering
[65
], to determine the accuracy of templates required
[20
], and to calculate the false alarm probability and
thresholds
[41
]
. An important point is the reduction of the number of parameters
that one needs to search for in order to detect a signal. Namely
estimators of a certain type of parameters, called
extrinsic parameters, can be found in a closed analytic form and consequently
eliminated from the search. Thus a computationally intensive
search needs only be performed over a reduced set of
intrinsic
parameters
[48, 41
, 50
]
.
Techniques reviewed in this paper have been
used in the data analysis of prototypes of gravitational-wave
detectors
[64, 62, 6]
and in the data analysis of presently working gravitational-wave
detectors
[77, 12, 3
, 2, 1
]
.
We use units such that the velocity of light
.
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