Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation

Abstract

Inspiraling compact binaries are promising sources of gravitational waves for ground and space-based laser interferometric detectors. The time-dependent signature of these sources in the detectors is a well-characterized function of a relatively small number of parameters; thus, the favored analysis technique makes use of matched filtering and maximum likelihood methods. Current analysis methodology samples the matched filter output at parameter values chosen so that the correlation between successive samples is 97% for which the filtered output is closely correlated. Here we describe a straightforward and practical way of using interpolation to take advantage of the correlation between the matched filter output associated with nearby points in the parameter space to significantly reduce the number of matched filter evaluations without sacrificing the efficiency with which real signals are recognized. Because the computational cost of the analysis is driven almost exclusively by the matched filter evaluations, this translates directly into an increase in computational efficiency, which in turn, translates into an increase in the size of the parameter space that can be analyzed and, thus, the science that can be accomplished with the data. As a demonstration we compare the present "dense sampling" analysis methodology with our proposed "interpolation" methodology, restricted to one dimension of the multi-dimensional analysis problem. We find that the interpolated search reduces by 25% the number of filter evaluations required by the dense search with 97% correlation to achieve the same efficiency of detection for an expected false alarm probability. Generalized to higher dimensional space of a generic binary including spins suggests an order of magnitude increase in computational efficiency.