On the estimation of parameters of the gravitational-wave signal from a coalescing binary by a network of detectors

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Estimation of parameters of the gravitational-wave signal from a coalescing binary by a network of laser interferometers is considered. A solution of the inverse problem for the network of three detectors is generalized to the network of N detectors. This enables, from measurements at individual detectors of the network, optimal estimation of the astrophysically interesting parameters of the binary system: its distance from Earth, its position in the sky, and the chirp mass of the system. Maximum likelihood and least-squares methods are used to obtain the solution. The existence of the solution in view of the nonlinear nature of the problem and the noise in the detectors is discussed. An alternative solution of the inverse problem that circumvents the singularities present in the problem is proposed. Accuracy of the estimation of the parameters is assessed from the inverse of the Fisher information matrix. The variance of the maximum likelihood estimator of the distance is calculated for a simple model and compared with the approximate one obtained from the Fisher matrix. Extensive Monte Carlo simulations are performed to assess the accuracy of the estimation of the astrophysical parameters by networks of three and four detectors. Addition of the fourth detector to the network markedly improves the performance of the network. Adding the fourth node in Australia to the LIGO/VIRGO network increases the number of detectable events roughly twofold. For the four-detector network one can find among all detectable events again roughly twice the number of events for which accurate determination of the binary distance is possible. Moreover, the position of the binary in the sky can be typically determined three to four times more accurately for the enhanced LIGO/VIRGO network.