ON THE ESTIMATION OF PARAMETERS OF THE GRAVITATIONAL-WAVE SIGNAL FROMA COALESCING BINARY BY A NETWORK OF DETECTORS

Estimation of parameters of the gravitational-wave signal from a coale scing binary by a network of laser interferometers is considered. A so lution of the inverse problem for the network of three detectors is ge neralized to the network of N detectors. This enables, from measuremen ts at individual detectors of the network, optimal estimation of the a strophysically interesting parameters of the binary system: its distan ce from Earth, its position in the sky, and the chirp mass of the syst em. Maximum likelihood and least-squares methods are used to obtain th e solution. The existence of the solution in view of the nonlinear nat ure of the problem and the noise in the detectors is discussed. An alt ernative solution of the inverse problem that circumvents the singular ities present in the problem is proposed. Accuracy of the estimation o f the parameters is assessed from the inverse of the Fisher informatio n matrix. The variance of the maximum likelihood estimator of the dist ance is calculated for a simple model and compared with the approximat e one obtained from the Fisher matrix. Extensive Monte Carlo simulatio ns are performed to assess the accuracy of the estimation of the astro physical parameters by networks of three and four detectors. Addition of the fourth detector to the network markedly improves the performanc e of the network. Adding the fourth node in Australia to the LIGO/VIRG O network increases the number of detectable events roughly twofold. F or the four-detector network one can find among all detectable events again roughly twice the number of events for which accurate determinat ion 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.