17,400 research outputs found
Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic
We discuss a robust data analysis method to detect a stochastic background of
gravitational waves in the presence of non-Gaussian noise. In contrast to the
standard cross-correlation (SCC) statistic frequently used in the stochastic
background searches, we consider a {\it generalized cross-correlation} (GCC)
statistic, which is nearly optimal even in the presence of non-Gaussian noise.
The detection efficiency of the GCC statistic is investigated analytically,
particularly focusing on the statistical relation between the false-alarm and
the false-dismissal probabilities, and the minimum detectable amplitude of
gravitational-wave signals. We derive simple analytic formulae for these
statistical quantities. The robustness of the GCC statistic is clarified based
on these formulae, and one finds that the detection efficiency of the GCC
statistic roughly corresponds to the one of the SCC statistic neglecting the
contribution of non-Gaussian tails. This remarkable property is checked by
performing the Monte Carlo simulations and successful agreement between
analytic and simulation results was found.Comment: 15 pages, 8 figures, presentation and some figures modified, final
version to be published in PR
Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise I: Frequentist analyses
Gravitational wave detectors will need optimal signal-processing algorithms
to extract weak signals from the detector noise. Most algorithms designed to
date are based on the unrealistic assumption that the detector noise may be
modeled as a stationary Gaussian process. However most experiments exhibit a
non-Gaussian ``tail'' in the probability distribution. This ``excess'' of large
signals can be a troublesome source of false alarms. This article derives an
optimal (in the Neyman-Pearson sense, for weak signals) signal processing
strategy when the detector noise is non-Gaussian and exhibits tail terms. This
strategy is robust, meaning that it is close to optimal for Gaussian noise but
far less sensitive than conventional methods to the excess large events that
form the tail of the distribution. The method is analyzed for two different
signal analysis problems: (i) a known waveform (e.g., a binary inspiral chirp)
and (ii) a stochastic background, which requires a multi-detector signal
processing algorithm. The methods should be easy to implement: they amount to
truncation or clipping of sample values which lie in the outlier part of the
probability distribution.Comment: RevTeX 4, 17 pages, 8 figures, typos corrected from first version
Detection methods for non-Gaussian gravitational wave stochastic backgrounds
We address the issue of finding an optimal detection method for a
discontinuous or intermittent gravitational wave stochastic background. Such a
signal might sound something like popcorn popping. We derive an appropriate
version of the maximum likelihood detection statistic, and compare its
performance to that of the standard cross-correlation statistic both
analytically and with Monte Carlo simulations. The maximum likelihood statistic
performs better than the cross-correlation statistic when the background is
sufficiently non-Gaussian. For both ground and space based detectors, this
results in a gain factor, ranging roughly from 1 to 3, in the minimum
gravitational-wave energy density necessary for detection, depending on the
duty cycle of the background. Our analysis is exploratory, as we assume that
the time structure of the events cannot be resolved, and we assume white,
Gaussian noise in two collocated, aligned detectors. Before this detection
method can be used in practice with real detector data, further work is
required to generalize our analysis to accommodate separated, misaligned
detectors with realistic, colored, non-Gaussian noise.Comment: 25 pages, 12 figures, submitted to physical review D, added revisions
in response to reviewers comment
The optimal search for an astrophysical gravitational-wave background
Roughly every 2-10 minutes, a pair of stellar mass black holes merge
somewhere in the Universe. A small fraction of these mergers are detected as
individually resolvable gravitational-wave events by advanced detectors such as
LIGO and Virgo. The rest contribute to a stochastic background. We derive the
statistically optimal search strategy for a background of unresolved binaries.
Our method applies Bayesian parameter estimation to all available data. Using
Monte Carlo simulations, we demonstrate that the search is both "safe" and
effective: it is not fooled by instrumental artefacts such as glitches, and it
recovers simulated stochastic signals without bias. Given realistic
assumptions, we estimate that the search can detect the binary black hole
background with about one day of design sensitivity data versus
months using the traditional cross-correlation search. This framework
independently constrains the merger rate and black hole mass distribution,
breaking a degeneracy present in the cross-correlation approach. The search
provides a unified framework for population studies of compact binaries, which
is cast in terms of hyper-parameter estimation. We discuss a number of
extensions and generalizations including: application to other sources (such as
binary neutron stars and continuous-wave sources), simultaneous estimation of a
continuous Gaussian background, and applications to pulsar timing.Comment: 16 pages, 9 figure
Echo Cancellation : the generalized likelihood ratio test for double-talk vs. channel change
Echo cancellers are required in both electrical (impedance mismatch) and acoustic (speaker-microphone coupling) applications. One of the main design problems is the control logic for adaptation. Basically, the algorithm weights should be frozen in the presence of double-talk and adapt quickly in the absence of double-talk. The optimum likelihood ratio test (LRT) for this problem was studied in a recent paper. The LRT requires a priori knowledge of the background noise and double-talk power levels. Instead, this paper derives a generalized log likelihood ratio test (GLRT) that does not require this knowledge. The probability density function of a sufficient statistic under each hypothesis is obtained and the performance of the test is evaluated as a function of the system parameters. The receiver operating characteristics (ROCs) indicate that it is difficult to correctly decide between double-talk and a channel change, based upon a single look. However, detection based on about 200 successive samples yields a detection probability close to unity (0.99) with a small false alarm probability (0.01) for the theoretical GLRT model. Application of a GLRT-based echo canceller (EC) to real voice data shows comparable performance to that of the LRT-based EC given in a recent paper
Parametric modeling of photometric signals
This paper studies a new model for photometric signals under high flux assumption. Photometric signals are modeled by Gaussian autoregressive processes having the same mean and variance denoted Constraint Gaussian Autoregressive Processes (CGARP's). The estimation of the CGARP parameters is discussed. The CramĂ©r Rao lower bounds for these parameters are studied and compared to the estimator mean square errors. The CGARP is intended to model the signal received by a satellite designed for extrasolar planets detection. A transit of a planet in front of a star results in an abrupt change in the mean and variance of the CGARP. The NeymanâPearson detector for this changepoint detection problem is derived when the abrupt change parameters are known. Closed form expressions for the Receiver Operating Characteristics (ROC) are provided. The NeymanâPearson detector combined with the maximum likelihood estimator for CGARP parameters allows to study the generalized likelihood ratio detector. ROC curves are then determined using computer simulations
Gravitational waves: search results, data analysis and parameter estimation
The Amaldi 10 Parallel Session C2 on gravitational wave (GW) search results, data analysis and parameter estimation included three lively sessions of lectures by 13 presenters, and 34 posters. The talks and posters covered a huge range of material, including results and analysis techniques for ground-based GW detectors, targeting anticipated signals from different astrophysical sources: compact binary inspiral, merger and ringdown; GW bursts from intermediate mass binary black hole mergers, cosmic string cusps, core-collapse supernovae, and other unmodeled sources; continuous waves from spinning neutron stars; and a stochastic GW background. There was considerable emphasis on Bayesian techniques for estimating the parameters of coalescing compact binary systems from the gravitational waveforms extracted from the data from the advanced detector network. This included methods to distinguish deviations of the signals from what is expected in the context of General Relativity
Fisher-information condition for enhanced signal detection via stochastic resonance
Various situations where a signal is enhanced by noise through stochastic resonance are now known. This paper contributes to determining general conditions under which improvement by noise can be a priori decided as feasible or not. We focus on the detection of a known signal in additive white noise. Under the assumptions of a weak signal and a sufficiently large sample size, it is proved, with an inequality based on the Fisher information, that improvement by adding noise is never possible, generically, in these conditions. However, under less restrictive conditions, an example of signal detection is shown with favorable action of adding noise.Fabing Duan, François Chapeau-Blondeau, Derek Abbot
Detecting a gravitational-wave background with next-generation space interferometers
Future missions of gravitational-wave astronomy will be operated by
space-based interferometers, covering very wide range of frequency. Search for
stochastic gravitational-wave backgrounds (GWBs) is one of the main targets for
such missions, and we here discuss the prospects for direct measurement of
isotropic and anisotropic components of (primordial) GWBs around the frequency
0.1-10 Hz. After extending the theoretical basis for correlation analysis, we
evaluate the sensitivity and the signal-to-noise ratio for the proposed future
space interferometer missions, like Big-Bang Observer (BBO), Deci-Hertz
Interferometer Gravitational-wave Observer (DECIGO) and recently proposed
Fabry-Perot type DECIGO. The astrophysical foregrounds which are expected at
low frequency may be a big obstacle and significantly reduce the
signal-to-noise ratio of GWBs. As a result, minimum detectable amplitude may
reach h^2 \ogw = 10^{-15} \sim 10^{-16}, as long as foreground point sources
are properly subtracted. Based on correlation analysis, we also discuss
measurement of anisotropies of GWBs. As an example, the sensitivity level
required for detecting the dipole moment of GWB induced by the proper motion of
our local system is closely examined.Comment: 19 pages, 6 figures, references added, typos correcte
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