Optimal detection of burst events in gravitational wave interferometric observatories

We consider the problem of detecting a burst signal of unknown shape. We introduce a statistic which generalizes the excess power statistic proposed by Flanagan and Hughes and extended by Anderson et al. The statistic we propose is shown to be optimal for arbitrary noise spectral characteristic, under the two hypotheses that the noise is Gaussian, and that the prior for the signal is uniform. The statistic derivation is based on the assumption that a signal affects only affects N samples in the data stream, but that no other information is a priori available, and that the value of the signal at each sample can be arbitrary. We show that the proposed statistic can be implemented combining standard time-series analysis tools which can be efficiently implemented, and the resulting computational cost is still compatible with an on-line analysis of interferometric data. We generalize this version of an excess power statistic to the multiple detector case, also including the effect of correlated noise. We give full details about the implementation of the algorithm, both for the single and the multiple detector case, and we discuss exact and approximate forms, depending on the specific characteristics of the noise and on the assumed length of the burst event. As a example, we show what would be the sensitivity of the network of interferometers to a delta-function burst.Comment: 21 pages, 5 figures in 3 groups. Submitted for publication to Phys.Rev.D. A Mathematica notebook is available at http://www.ligo.caltech.edu/~avicere/nda/burst/Burst.nb which allows to reproduce the numerical results of the pape

Optimal generalization of power filters for gravitational wave bursts, from single to multiple detectors

Searches for gravitational wave signals which do not have a precise model describing the shape of their waveforms are often performed using power detectors based on a quadratic form of the data. A new, optimal method of generalizing these power detectors so that they operate coherently over a network of interferometers is presented. Such a mode of operation is useful in obtaining better detection efficiencies, and better estimates of the position of the source of the gravitational wave signal. Numerical simulations based on a realistic, computationally efficient hierarchical implementation of the method are used to characterize its efficiency, for detection and for position estimation. The method is shown to be more efficient at detecting signals than an incoherent approach based on coincidences between lists of events. It is also shown to be capable of locating the position of the source.Comment: 16 pages, 5 figure

A learning approach to the detection of gravitational wave transients

We investigate the class of quadratic detectors (i.e., the statistic is a bilinear function of the data) for the detection of poorly modeled gravitational transients of short duration. We point out that all such detection methods are equivalent to passing the signal through a filter bank and linearly combine the output energy. Existing methods for the choice of the filter bank and of the weight parameters rely essentially on the two following ideas: (i) the use of the likelihood function based on a (possibly non-informative) statistical model of the signal and the noise, (ii) the use of Monte-Carlo simulations for the tuning of parametric filters to get the best detection probability keeping fixed the false alarm rate. We propose a third approach according to which the filter bank is "learned" from a set of training data. By-products of this viewpoint are that, contrarily to previous methods, (i) there is no requirement of an explicit description of the probability density function of the data when the signal is present and (ii) the filters we use are non-parametric. The learning procedure may be described as a two step process: first, estimate the mean and covariance of the signal with the training data; second, find the filters which maximize a contrast criterion referred to as deflection between the "noise only" and "signal+noise" hypothesis. The deflection is homogeneous to the signal-to-noise ratio and it uses the quantities estimated at the first step. We apply this original method to the problem of the detection of supernovae core collapses. We use the catalog of waveforms provided recently by Dimmelmeier et al. to train our algorithm. We expect such detector to have better performances on this particular problem provided that the reference signals are reliable.Comment: 22 pages, 4 figure

Detection in coincidence of gravitational wave bursts with a network of interferometric detectors (I): Geometric acceptance and timing

Detecting gravitational wave bursts (characterised by short durations and poorly modelled waveforms) requires to have coincidences between several interferometric detectors in order to reject non-stationary noise events. As the wave amplitude seen in a detector depends on its location with respect to the source direction and as the signal to noise ratio of these bursts are expected to be low, coincidences between antennas may not be so likely. This paper investigates this question from a statistical point of view by using a simple model of a network of detectors; it also estimates the timing precision of a detection in an interferometer which is an important issue for the reconstruction of the source location, based on time delays.Comment: low resolution figure 1 due to file size problem

About the detection of gravitational wave bursts

Several filtering methods for the detection of gravitational wave bursts in interferometric detectors are presented. These are simple and fast methods which can act as online triggers. All methods are compared to matched filtering with the help of a figure of merit based on the detection of supernovae signals simulated by Zwerger and Muller.Comment: 5 pages, proceedings of GWDAW99 (Roma, Dec. 1999), to appear in Int. J. Mod. Phys.

Time-frequency detection algorithm for gravitational wave bursts

An efficient algorithm is presented for the identification of short bursts of gravitational radiation in the data from broad-band interferometric detectors. The algorithm consists of three steps: pixels of the time-frequency representation of the data that have power above a fixed threshold are first identified. Clusters of such pixels that conform to a set of rules on their size and their proximity to other clusters are formed, and a final threshold is applied on the power integrated over all pixels in such clusters. Formal arguments are given to support the conjecture that this algorithm is very efficient for a wide class of signals. A precise model for the false alarm rate of this algorithm is presented, and it is shown using a number of representative numerical simulations to be accurate at the 1% level for most values of the parameters, with maximal error around 10%.Comment: 26 pages, 15 figures, to appear in PR

An efficient filter for detecting gravitational wave bursts in interferometric detectors

Typical sources of gravitational wave bursts are supernovae, for which no accurate models exist. This calls for search methods with high efficiency and robustness to be used in the data analysis of foreseen interferometric detectors. A set of such filters is designed to detect gravitational wave burst signals. We first present filters based on the linear fit of whitened data to short straight lines in a given time window and combine them in a non linear filter named ALF. We study the performances and efficiencies of these filters, with the help of a catalogue of simulated supernova signals. The ALF filter is the most performant and most efficient of all filters. Its performance reaches about 80% of the Optimal Filter performance designed for the same signals. Such a filter could be implemented as an online trigger (dedicated to detect bursts of unknown waveform) in interferometric detectors of gravitational waves

On line power spectra identification and whitening for the noise in interferometric gravitational wave detectors

In this paper we address both to the problem of identifying the noise Power Spectral Density of interferometric detectors by parametric techniques and to the problem of the whitening procedure of the sequence of data. We will concentrate the study on a Power Spectral Density like the one of the Italian-French detector VIRGO and we show that with a reasonable finite number of parameters we succeed in modeling a spectrum like the theoretical one of VIRGO, reproducing all its features. We propose also the use of adaptive techniques to identify and to whiten on line the data of interferometric detectors. We analyze the behavior of the adaptive techniques in the field of stochastic gradient and in the Least Squares ones.Comment: 28 pages, 21 figures, uses iopart.cls accepted for pubblication on Classical and Quantum Gravit

Mass hierarchy discrimination with atmospheric neutrinos in large volume ice/water Cherenkov detectors

Large mass ice/water Cherenkov experiments, optimized to detect low energy (1-20 GeV) atmospheric neutrinos, have the potential to discriminate between normal and inverted neutrino mass hierarchies. The sensitivity depends on several model and detector parameters, such as the neutrino flux profile and normalization, the Earth density profile, the oscillation parameter uncertainties, and the detector effective mass and resolution. A proper evaluation of the mass hierarchy discrimination power requires a robust statistical approach. In this work, the Toy Monte Carlo, based on an extended unbinned likelihood ratio test statistic, was used. The effect of each model and detector parameter, as well as the required detector exposure, was then studied. While uncertainties on the Earth density and atmospheric neutrino flux profiles were found to have a minor impact on the mass hierarchy discrimination, the flux normalization, as well as some of the oscillation parameter (\Delta m^2_{31}, \theta_{13}, \theta_{23}, and \delta_{CP}) uncertainties and correlations resulted critical. Finally, the minimum required detector exposure, the optimization of the low energy threshold, and the detector resolutions were also investigated.Comment: 23 pages, 16 figure

Testing the performance of a blind burst statistic

In this work we estimate the performance of a method for the detection of burst events in the data produced by interferometric gravitational wave detectors. We compute the receiver operating characteristics in the specific case of a simulated noise having the spectral density expected for Virgo, using test signals taken from a library of possible waveforms emitted during the collapse of the core of Type II Supernovae.Comment: 8 pages, 6 figures, Talk given at the GWDAW2002 worksho