Searching for gravitational waves from known pulsars using the F and G statistics

In search for gravitational waves emitted by known isolated pulsars in data collected by a detector, one can assume that the frequency of the wave, its spindown parameters and the position of the source in the sky are known, and so the almost monochromatic gravitational-wave signal we are looking for depends on at the most four parameters: overall amplitude, initial phase, polarization angle and inclination angle of the pulsar's rotation axis with respect to the line of sight. We derive two statistics by means of which one can test whether data contain such gravitational-wave signals: the G-statistic for signals which depend on only two unknown parameters (overall amplitude and initial phase), and the F-statistic for signals depending on all four parameters. We study, by means of the Fisher matrix, the theoretical accuracy of the maximum-likelihood estimators of the signal's parameters and we present the results of the Monte Carlo simulations we performed to test the accuracy of these estimators.