Statistical analysis of the estimators of the parameters of the gravitational-wave signal from a coalescing binary

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Abstract
Matched filtering is proposed as a way to detect the gravitational-wave signal from a coalescing binary and to estimate its parameters. One of the authors (AK) has investigated the theoretical performance of this method by calculating the signal-to-noise ratio and the covariance matrix for the parameters of the signal. In this work we try to verify how the above method will work in practice. We generate a Gaussian, approximately white noise and add the signal, and then, using the algorithm derived from the maximum likelihood principle, we find the maximum likelihood estimators of the parameters. The procedure amounts essentially to the maximization of the correlation of the data with the filter matched to the signal. The size of the maximum of the correlation determines the probability of the detection of the signal. We repeat the procedure a thousand times to obtain suitable statistics for the estimators. We find that it agrees well with the theoretical predictions. We also investigate the post-Newtonian effects. It was recently shown by the Caltech group that the matched filtering technique is sensitive to the post-Newtonian corrections. We demonstrate this by inputing the signal with the first post-Newtonian term and correlating the data with the Newtonian filter. We find that we can still detect the post-Newtonian signal with a Newtonian filter but the maximum of the correlation falls by 40% and consequently the probability of the detection decreases. The estimates of the mass parameter of the post-Newtonian signal and its time-of-arrival are shifted by a certain amount from the true values. We also address the problem of the estimation of the individual masses of the binary.