Solution to the inverse problem for a noisy spherical gravitational wave antenna

Details Solution to the inverse problem for a noisy spherical gravitational wave antenna Solution to the inverse problem for a noisy spherical gravitational wave antenna

1997-12-18

arxiv.org/abs/gr-qc/9712079v2

Phys.Rev.D58:062002,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 3 figures, to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.58.062002

A spherical gravitational wave antenna is distinct from other types of gravitational wave antennas in that only a single detector is necessary to determine the direction and polarization of a gravitational wave. Zhou and Michelson showed that the inverse problem can be solved using the maximum likelihood method if the detector outputs are independent and have normally distributed noise with the same variance. This paper presents an analytic solution using only linear algebra that is found to produce identical results as the maximum likelihood method but with less computational burden. Applications of this solution to gravitational waves in alternative symmetric metric theories of gravity and impulsive excitations also are discussed.

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