In this section, we study the detection of a deterministic gravitational-wave signal of the general form given by Eq. (32) and the estimation of its parameters using the maximum-likelihood (ML) principle. We assume that the noise in the detector is a zero-mean, Gaussian, and stationary random process. The data in the detector, in the case when the gravitational-wave signal is present, is . The parameters of the signal (32) split into extrinsic (or amplitude) parameters and intrinsic ones .

4.1 The -statistic

4.1.1 Targeted searches

4.2 Signal-to-noise ratio and the Fisher matrix

4.3 False alarm and detection probabilities

4.3.1 False alarm and detection probabilities for known intrinsic parameters

4.3.2 False alarm probability for unknown intrinsic parameters

4.3.3 Detection probability for unknown intrinsic parameters

4.4 Number of templates

4.4.1 Covering problem

4.5 Suboptimal filtering

4.6 Algorithms to calculate the -statistic

4.6.1 The two-step procedure

4.6.2 Evaluation of the -statistic

4.7 Accuracy of parameter estimation

4.7.1 Fisher-matrix-based assessments

4.7.2 Comparison with the Cramèr–Rao bound

4.8 Upper limits

4.1.1 Targeted searches

4.2 Signal-to-noise ratio and the Fisher matrix

4.3 False alarm and detection probabilities

4.3.1 False alarm and detection probabilities for known intrinsic parameters

4.3.2 False alarm probability for unknown intrinsic parameters

4.3.3 Detection probability for unknown intrinsic parameters

4.4 Number of templates

4.4.1 Covering problem

4.5 Suboptimal filtering

4.6 Algorithms to calculate the -statistic

4.6.1 The two-step procedure

4.6.2 Evaluation of the -statistic

4.7 Accuracy of parameter estimation

4.7.1 Fisher-matrix-based assessments

4.7.2 Comparison with the Cramèr–Rao bound

4.8 Upper limits

Living Rev. Relativity 15, (2012), 4
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