Using weighting algorithms to refine source direction determinations in all-sky gravitational wave burst searches with two-detector networks

Abstract

I explore the possibility of resurrecting an old, non-Bayesian computational approach for inferring the source direction of a gravitational wave from the output of a two-detector network. The method gives the beam pattern response functions and time delay, and performs well even in the presence of noise and unexpected signal forms. I further suggest an improvement to this method in the form of a weighting algorithm that usefully improves its accuracy beyond what can be achieved with simple best-fit methods, validating the new procedure with several small-scale simulations. The approach is identified as complimentary to -rather than in competition with -the now-standard Bayesian approach typically used by the LIGO network in parameter determination. Finally, I briefly discuss the possible applications of this method in the world of three-or-more detector networks and some directions for future work.

Using weighting algorithms to refine source direction determinations in all-sky gravitational wave burst searches with two-detector networks II: The case of elliptical polarization

“…Naturally, the performance of a revised algorithm with weighting function f (Q/Q min ) depends entirely upon the function f . As in [1], I focus on weighting functions of the form…”

“…The algorithm's performance in determining τ is relatively close to this ideal. However, as seen in [1], higher frequency signals and higher maximum levels of noise and un-modeled signal reduce the accuracy of the method in finding beam F + and F × at the two sites. Though the algorithm suffers at higher frequenciesan effect likely due to the fact that even small non-zero values δτ are amplified by the frequency when determining the mismatch of eq.…”

“…As was concluded in [1], more extensive computational testing with a set of networked cores is still necessary to prove that the algorithm will continue to perform well once massively parallelized. The current simulation results continue to show promise, suggesting that the time and computing resources necessary for this more extensive testing would be well spent.…”

“…To extend my previous analysis, I continue to build upon the basic approach used in [1]. As before, I model the incoming waves with a sine-Gaussian waveform, as used by the LIGO collaboration in their all-sky burst search event detection algorithms [5].…”

“…In a recent paper [1] I suggested using weighting algorithms to revitalize a very old method of determining the source location of gravitational waves in allsky burst searches with two detector networks. The method begins by simply simulating a great many possible signals and looking for the one that produces the smallest deviation from the actual detector responses, but improves on the performance of that single-best-fit method by positing that, in the absence of any single excellent fit -as we must expect in the presence of substantial noise or if we do not wish to expend the extraordinary computational resources required to produce accurate results with high-performance Bayesian analysis methods like LALInference -it should be the sky angles that produce the largest number of better-than-average fits that represent the true source location.…”