In this review we consider the problem of detection of deterministic gravitational-wave signals in the noise of a detector and the question of estimation of their parameters. The examples of deterministic signals are gravitational waves from rotating neutron stars, coalescing compact binaries, and supernova explosions. The case of detection of stochastic gravitational-wave signals in the noise of a detector is reviewed in [8]. A very powerful method to detect a signal in noise that is optimal by several criteria consists of correlating the data with the template that is matched to the expected signal. This matched-filtering technique is a special case of the maximum likelihood detection method. In this review we describe the theoretical foundation of the method and we show how it can be applied to the case of a very general deterministic gravitational-wave signal buried in a stationary and Gaussian noise.
Early gravitational-wave data analysis was concerned with the detection of bursts originating from
supernova explosions [144]. It involved analysis of the coincidences among the detectors [70]. 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 [135] and that they can
provide a wealth of astrophysical information [122, 77]. For example, the analytic form of the
gravitational-wave signal produced during the inspiral phase of a compact binary coalescence is known in
terms of a few parameters to a good approximation (see, e.g., [30
] and Section 2.4 of [66
]).
Consequently one can detect such a signal by correlating the data with the predicted waveform (often
called the template) 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 [135
]. This observation has led to
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, 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 [123]. 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 [50, 76
]. 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 [41
, 75
, 25
]. It was also
realized that the 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 [124
].
A very important development was the work by Cutler et al. [43] 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 development of the theory, methods
were introduced to calculate the quality of suboptimal filters [13], to calculate the number of
templates required to do a search using matched-filtering [102
], to determine the accuracy of
templates required [33
], and to calculate the false alarm probability and thresholds [68
]. 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 need only be performed over a reduced set of intrinsic
parameters [76
, 68
, 78
].
Techniques reviewed in this paper have been used in the data analysis of prototypes of
gravitational-wave detectors [100, 99, 12] and in the data analysis of gravitational-wave detectors currently
in operation [133, 23, 4
, 3, 2
].
http://www.livingreviews.org/lrr-2012-4 |
Living Rev. Relativity 15, (2012), 4
![]() This work is licensed under a Creative Commons License. E-mail us: |