For the general gravitational-wave signal
defined in Equation (12) 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 (32
), 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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