author = "Costa, Carlos Filipe da Silva and Magalh{\~a}es, Nadja S.",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and 
                         {Universidade Federal de S{\~a}o Paulo (UNIFESP)}",
                title = "Overcoming analytic solution limitations in gravitational wave 
                         direction determination",
              journal = "Classical and Quantum Gravity",
                 year = "2015",
               volume = "32",
               number = "095006",
                month = "1-18",
             keywords = "Direction reconstruction, Gravitational waves, Inverse problem, 
                         Low latency analysis.",
             abstract = "Determining the direction of a gravitational wave (GW) source is 
                         necessary for confrontations between a candidate GW signal and its 
                         electromagnetic counterpart. In the context of low latency 
                         pipelines it is assumed that analytic solutions (based on the GW 
                         matrix reconstruction) can efficiently provide the GW direction. 
                         However, we identified that such analytic solutions present 
                         theoretical and practical limitations (indeterminacies) which were 
                         not previously mentioned in the literature. Under realistic 
                         conditions, we identified that for certain incoming directions, 
                         such solutions are unable to recover them. Therefore, we provide 
                         here for the first time a full review of these indeterminacy cases 
                         and explain their origins. We then propose a mathematical 
                         procedure that reduces such indeterminacies. Taking into account 
                         the constraining requirements of a low latency pipeline, we 
                         developed a method that requires the least computational power to 
                         retrieve GW directions. The mathematical considerations and method 
                         principle can be applied to any system of detectors able to 
                         reconstruct the GW matrix. We tested it on simulated data of the 
                         Schenberg GW detector. The results show that this method cancels 
                         out indeterminacies and the direction resolution \σ 
                         (\δs) is limited by a 1/SNR law for any incoming direction. 
                         Thus it retrieves a remarkable advantage of the spherical GW 
                         antenna: the possibility of an isotropic direction 
                  doi = "10.1088/0264-9381/32/9/095006",
                  url = "http://dx.doi.org/10.1088/0264-9381/32/9/095006",
                 issn = "0264-9381",
             language = "en",
           targetfile = "silva costa_overcoming.pdf",
        urlaccessdate = "18 jan. 2021"