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

TL;DR

This paper introduces a linear algebra-based analytic solution for the inverse problem in spherical gravitational wave antennas, simplifying computations while maintaining accuracy, and explores applications in alternative gravity theories and impulsive signals.

Contribution

It provides a new, less computationally intensive analytic method for solving the inverse problem in spherical gravitational wave detectors, replacing the maximum likelihood approach.

Findings

Analytic solution matches maximum likelihood results

Reduced computational complexity

Applicable to alternative gravity theories and impulsive signals

Abstract

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.