For the general gravitational-wave signal defined in Equation (14) the log likelihood function is given by
Thus the procedure to detect the signal and estimate its parameters consists of two parts. The first part is to find the (local) maxima of the -statistic in the intrinsic parameter space. The ML estimators of the intrinsic parameters are those for which the -statistic attains a maximum. The second part is to calculate the estimators of the extrinsic parameters from the analytic formula (34), where the matrix and the correlations are calculated for the intrinsic parameters equal to their ML estimators obtained from the first part of the analysis. We call this procedure the maximum likelihood detection. See Section 4.8 for a discussion of the algorithms to find the (local) maxima of the -statistic.
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