7 research outputs found
Correlator Bank Detection of GW chirps. False-Alarm Probability, Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue
The general problem of computing the false-alarm rate vs. detection-threshold
relationship for a bank of correlators is addressed, in the context of
maximum-likelihood detection of gravitational waves, with specific reference to
chirps from coalescing binary systems. Accurate (lower-bound) approximants for
the cumulative distribution of the whole-bank supremum are deduced from a class
of Bonferroni-type inequalities. The asymptotic properties of the cumulative
distribution are obtained, in the limit where the number of correlators goes to
infinity. The validity of numerical simulations made on small-size banks is
extended to banks of any size, via a gaussian-correlation inequality. The
result is used to estimate the optimum template density, yielding the best
tradeoff between computational cost and detection efficiency, in terms of
undetected potentially observable sources at a prescribed false-alarm level,
for the simplest case of Newtonian chirps.Comment: submitted to Phys. Rev.
Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing Binary Gravitational Wave Signals
A global network of laser interferometric gravitational wave detectors is
projected to be in operation by around the turn of the century. Here, the noisy
output of a single instrument is examined. A gravitational wave is assumed to
have been detected in the data and we deal with the subsequent problem of
parameter estimation. Specifically, we investigate theoretical lower bounds on
the minimum mean-square errors associated with measuring the parameters of the
inspiral waveform generated by an orbiting system of neutron stars/black holes.
Three theoretical lower bounds on parameter estimation accuracy are considered:
the Cramer-Rao bound (CRB); the Weiss-Weinstein bound (WWB); and the Ziv-Zakai
bound (ZZB). We obtain the WWB and ZZB for the Newtonian-form of the coalescing
binary waveform, and compare them with published CRB and numerical Monte-Carlo
results. At large SNR, we find that the theoretical bounds are all identical
and are attained by the Monte-Carlo results. As SNR gradually drops below 10,
the WWB and ZZB are both found to provide increasingly tighter lower bounds
than the CRB. However, at these levels of moderate SNR, there is a significant
departure between all the bounds and the numerical Monte-Carlo results.Comment: 17 pages (LaTeX), 4 figures. Submitted to Physical Review
On Estimation of the Post-Newtonian Parameters in the Gravitational-Wave Emission of a Coalescing Binary
The effect of the recently obtained 2nd post-Newtonian corrections on the
accuracy of estimation of parameters of the gravitational-wave signal from a
coalescing binary is investigated. It is shown that addition of this correction
degrades considerably the accuracy of determination of individual masses of the
members of the binary. However the chirp mass and the time parameter in the
signal is still determined to a very good accuracy. The possibility of
estimation of effects of other theories of gravity is investigated. The
performance of the Newtonian filter is investigated and it is compared with
performance of post-Newtonian search templates introduced recently. It is shown
that both search templates can extract accurately useful information about the
binary.Comment: 34 pages, 118Kb, LATEX format, submitted to Phys. Rev.