Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case

Abstract

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, [Formula: see text]-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.

Figure 1

Schematic configuration of three freely falling masses as a detector of gravitational waves. The masses are labelled 1, 2, and 3, their positions with respect to the origin O of the coordinate system are given by vectors x_a (a = 1, 2, 3). The Euclidean separations between the masses are denoted by L_a, where the index a corresponds to the opposite mass. The unit vectors n_a point between pairs of masses, with the orientation indicated.