  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.
