Astronomical observations with a network of detectors of gravitational waves – II. Solution to the four and three detector problem

Abstract

In the theory of gravitational wave detection an important problem is the so-called inverse problem. It consists of determining the wave parameters from the responses of a suitable network of detectors. In this paper we solve the inverse problem with a network of (a) four detectors, and (b) three detectors, all located in the same place when the gravitational-wave signal is a burst with arbitrary polarization. We obtain from the four or three response amplitudes of the detectors the direction and the two amplitudes of the wave corresponding to the two independent polarizations. We use the mathematical framework developed in an earlier paper (Dhurandhar & Tinto). Non-linearities appear when there are less than five detectors, leading to spurious solutions which have to be weeded out.