Aperture synthesis for gravitational-wave data analysis: Deterministic Sources

Gravitational wave detectors now under construction are sensitive to the phase of the incident gravitational waves. Correspondingly, the signals from the different detectors can be combined, in the analysis, to simulate a single detector of greater amplitude and directional sensitivity: in short, aperture synthesis. Here we consider the problem of aperture synthesis in the special case of a search for a source whose waveform is known in detail: \textit{e.g.,} compact binary inspiral. We derive the likelihood function for joint output of several detectors as a function of the parameters that describe the signal and find the optimal matched filter for the detection of the known signal. Our results allow for the presence of noise that is correlated between the several detectors. While their derivation is specialized to the case of Gaussian noise we show that the results obtained are, in fact, appropriate in a well-defined, information-theoretic sense even when the noise is non-Gaussian in character. The analysis described here stands in distinction to ``coincidence analyses'', wherein the data from each of several detectors is studied in isolation to produce a list of candidate events, which are then compared to search for coincidences that might indicate common origin in a gravitational wave signal. We compare these two analyses --- optimal filtering and coincidence --- in a series of numerical examples, showing that the optimal filtering analysis always yields a greater detection efficiency for given false alarm rate, even when the detector noise is strongly non-Gaussian.Comment: 39 pages, 4 figures, submitted to Phys. Rev.

Robust Gravitational Wave Burst Detection and Source Localization in a Network of Interferometers Using Cross Wigner Spectra

We discuss a fast cross-Wigner transform based technique for detecting gravitational wave bursts, and estimating the direction of arrival, using a network of (three) non co-located interferometric detectors. The performances of the detector as a function of signal strength and source location, and the accuracy of the direction of arrival estimation are investigated by numerical simulations.Comment: accepted in Class. Quantum Gravit

Search strategies for long gravitational-wave transients: hidden Markov model tracking and seedless clustering

A number of detections have been made in the past few years of gravitational waves from compact binary coalescences. While there exist well-understood waveform models for signals from compact binary coalescences, many sources of gravitational waves are not well modeled, including potential long-transient signals from a binary neutron star post-merger remnant. Searching for these sources requires robust detection algorithms that make minimal assumptions about any potential signals. In this paper, we compare two unmodeled search schemes for long-transient gravitational waves, operating on cross-power spectrograms. One is an efficient algorithm first implemented for continuous wave searches, based on a hidden Markov model. The other is a seedless clustering method, which has been used in transient gravitational wave analysis in the past. We quantify the performance of both algorithms, including sensitivity and computational cost, by simulating synthetic signals with a special focus on sources like binary neutron star post-merger remnants. We demonstrate that the hidden Markov model tracking is a good option in model-agnostic searches for low signal-to-noise ratio signals. We also show that it can outperform the seedless method for certain categories of signals while also being computationally more efficient.Comment: 10 pages, 7 figure

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

Likelihood-ratio ranking of gravitational-wave candidates in a non-Gaussian background

We describe a general approach to detection of transient gravitational-wave signals in the presence of non-Gaussian background noise. We prove that under quite general conditions, the ratio of the likelihood of observed data to contain a signal to the likelihood of it being a noise fluctuation provides optimal ranking for the candidate events found in an experiment. The likelihood-ratio ranking allows us to combine different kinds of data into a single analysis. We apply the general framework to the problem of unifying the results of independent experiments and the problem of accounting for non-Gaussian artifacts in the searches for gravitational waves from compact binary coalescence in LIGO data. We show analytically and confirm through simulations that in both cases the likelihood ratio statistic results in an improved analysis.Comment: 10 pages, 6 figure

Time-frequency detection of Gravitational Waves

We present a time-frequency method to detect gravitational wave signals in interferometric data. This robust method can detect signals from poorly modeled and unmodeled sources. We evaluate the method on simulated data containing noise and signal components. The noise component approximates initial LIGO interferometer noise. The signal components have the time and frequency characteristics postulated by Flanagan and Hughes for binary black hole coalescence. The signals correspond to binaries with total masses between $45 M_\odot$ to $70 M_\odot$ and with (optimal filter) signal-to-noise ratios of 7 to 12. The method is implementable in real time, and achieves a coincident false alarm rate for two detectors $\approx$ 1 per 475 years. At this false alarm rate, the single detector false dismissal rate for our signal model is as low as 5.3% at an SNR of 10. We expect to obtain similar or better detection rates with this method for any signal of similar power that satisfies certain adiabaticity criteria. Because optimal filtering requires knowledge of the signal waveform to high precision, we argue that this method is likely to detect signals that are undetectable by optimal filtering, which is at present the best developed detection method for transient sources of gravitational waves.Comment: 24 pages, 5 figures, uses REVTE

Detection of gravitational wave bursts by interferometric detectors

We study in this paper some filters for the detection of burst-like signals in the data of interferometric gravitational-wave detectors. We present first two general (non-linear) filters with no {\it a priori} assumption on the waveforms to detect. A third filter, a peak correlator, is also introduced and permits to estimate the gain, when some prior information is known about the waveforms. We use the catalogue of supernova gravitational-wave signals built by Zwerger and M\"uller in order to have a benchmark of the performance of each filter and to compare to the performance of the optimal filter. The three filters could be a part of an on-line triggering in interferometric gravitational-wave detectors, specialised in the selection of burst events.Comment: 15 pages, 8 figure