<i>Statistical Theory Of Signal Detection</i>

Helstrom, Carl W.; Wilson, Fred L.

doi:10.1063/1.3022201

Cited by 478 publications

(356 citation statements)

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“…If the noise is assumed to be stationary and ergodic then there exists a noise correlation function K(t) such that C ij = K(|i − j|∆). In the Fourier basis it can be shown that the components of the noise vector are statistically independent [11] and the covariance matrix in the Fourier basis will contain only diagonal terms whose values will be strictly positive: C ii =ñ iñ * i . This implies that the covariance matrix has strictly positive eigenvalues.…”

Section: A Signal Manifoldmentioning

confidence: 99%

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Gravitational waves from coalescing binaries: Detection strategies and Monte Carlo estimation of parameters

1996

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The detection of gravitational waves from astrophysical sources is probably one of the most keenly awaited events in the history of astrophysics. The paucity of gravitational wave sources and the relative difficulty in detecting such waves, as compared to those in the electromagnetic domain, necessitate the development of optimal data analysis techniques to detect the signal, as well as to extract the maximum possible information from the detected signals. Coalescing binary systems are one of the most promising sources of gravitational waves. This is due to the fact that such sources are easier to model and thus one can design detection strategies particularly tuned to such signals. A lot of attention has been devoted in the literature studying such techniques and most of the work has revolved around the Weiner filtering and the maximum likelihood estimators of the parameters of the binary system. We investigate such techniques with the aid of differential geometry which provides geometric insight into the problem. Such a formalism allows to explore the merits and demerits of a detection scheme independent of the parameters chosen to represent the waveform. The formalism also generalises the problem of choosing an optimal set of templates to detect a known waveform buried in noisy data. We stress the need for finding a set of convenient parameters for the waveform and show that even after the inclusion of the second-order post-Newtonian corrections, the waveform can essentially be detected by employing a one-dimensional lattice of templates. This would be very useful both for the purpose of carrying out the simulations as well as for the actual detection process. After setting up such a formalism we carry out a Monte Carlo simulation of the detection process for the initial LIGO/VIRGO configuration for the first post-Newtonian corrected coalescing binary waveform. We compare the results of our simulations with the currently available estimates of the accuracies in the determination of the parameters and the probability distribution of the maximum likelihood estimators. Our results suggest that the covariance matrix underestimates, by over a factor of two, the actual errors in the estimation of parameters even when the signal-to-noise ratio is as high as 20. As only a tiny fraction of the events is expected to be detected with a signal-to-noise higher than this value, the covariance matrix is grossly inadequate to describe the errors in the measurement of the parameters of the waveform. It is found from our Monte Carlo simulations that the deviations from the covariance matrix are more in the case of the first post-Newtonian waveform than in the case of the Newtonian one. Inclusion of higher-order post-Newtonian corrections introduces new parameters that are correlated with those at the lower post-Newtonian waveform. Such correlations are expected to further increase the discrepancy of the covariance matrix results with those inferred from Monte Carlo simulations. Consequently, numerical simulations that take int...

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Section: A Signal Manifoldmentioning

confidence: 99%

“…Among them the technique of Weiner filtering is the most promising [10][11][12]. Briefly, this technique involves correlating the detector output with a set of templates, each of which is tuned to detect the signal with a particular set of parameters.…”

Section: Introductionmentioning

confidence: 99%

Gravitational waves from coalescing binaries: Detection strategies and Monte Carlo estimation of parameters

1996

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“…The approach is based on a matched filter technique for detecting a given signal of unknown phase in noisy data [Helstrom, 1968]. The technique consists of the following three steps: (1) Estimation of the noise power spectral density (PSD) of the data; (2) design of the matched filter; and (3) applying a threshold detector.…”

Section: Eddy Detectionmentioning

confidence: 99%

Eddies in the eastern Gulf of Alaska from TOPEX/POSEIDON altimetry

Meyers¹,

Basu²

1999

J. Geophys. Res.

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“…Among all filters, the best one is the Wiener (or matched) filter: it gives the highest SNR for a given signal [47] and has in addition the lowest false dismissal rate for a given threshold [48]. However, using it requires an accurate knowledge of the searched signal: as soon as the real signal and the template -i.e.…”

Section: A1 Filtering Methodsmentioning

confidence: 99%

Detection of a close supernova gravitational wave burst in a network of interferometers, neutrino and optical detectors

Arnaud

Barsuglia

Bizouard

et al. 2004

Astroparticle Physics

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Trying to detect the gravitational wave (GW) signal emitted by a type II supernova is a main challenge for the GW community. Indeed, the corresponding waveform is not accurately modeled as the supernova physics is very complex; in addition, all the existing numerical simulations agree on the weakness of the GW emission, thus restraining the number of sources potentially detectable. Consequently, triggering the GW signal with a confidence level high enough to conclude directly to a detection is very difficult, even with the use of a network of interferometric detectors. On the other hand, one can hope to take benefit from the neutrino and optical emissions associated to the supernova explosion, in order to discover and study GW radiation in an event already detected independently. This article aims at presenting some realistic scenarios for the search of the supernova GW bursts, based on the present knowledge of the emitted signals and on the results of network data analysis simulations. Both the direct search and the confirmation of the supernova event are considered. In addition, some physical studies following the discovery of a supernova GW emission are also mentioned: from the absolute neutrino mass to the supernova physics or the black hole signature, the potential spectrum of discoveries is wide.

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Statistical Theory Of Signal Detection

Cited by 478 publications

References 0 publications

Gravitational waves from coalescing binaries: Detection strategies and Monte Carlo estimation of parameters

Gravitational waves from coalescing binaries: Detection strategies and Monte Carlo estimation of parameters

Eddies in the eastern Gulf of Alaska from TOPEX/POSEIDON altimetry

Detection of a close supernova gravitational wave burst in a network of interferometers, neutrino and optical detectors

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