eng
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Living Reviews in Relativity
1433-8351
2012-03-09
15
4
10.12942/lrr-2012-4
lrr-2012-4
article
Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case
Piotr Jaranowski
1
Andrzej Królak
2
Institute of Theoretical Physics, University of Białystok, Lipowa 41, 15-424 Białystok, Poland
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warsaw, Poland
The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, ℱ-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.
http://www.livingreviews.org/lrr-2012-4
signal detection
parameter estimation
gravitational waves