Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing Binary Gravitational Wave Signals

TL;DR

This paper evaluates theoretical lower bounds on the accuracy of parameter estimation for gravitational wave signals from binary systems, comparing bounds and numerical results across different signal-to-noise ratios.

Contribution

It introduces and compares the Weiss-Weinstein and Ziv-Zakai bounds for gravitational wave parameter estimation, extending analysis beyond the traditional Cramer-Rao bound.

Findings

At high SNR, all bounds are identical and match Monte-Carlo results.

WWB and ZZB provide tighter bounds than CRB at moderate SNR levels.

Significant differences appear between bounds and Monte-Carlo results at low SNR.

Abstract

A global network of laser interferometric gravitational wave detectors is projected to be in operation by around the turn of the century. Here, the noisy output of a single instrument is examined. A gravitational wave is assumed to have been detected in the data and we deal with the subsequent problem of parameter estimation. Specifically, we investigate theoretical lower bounds on the minimum mean-square errors associated with measuring the parameters of the inspiral waveform generated by an orbiting system of neutron stars/black holes. Three theoretical lower bounds on parameter estimation accuracy are considered: the Cramer-Rao bound (CRB); the Weiss-Weinstein bound (WWB); and the Ziv-Zakai bound (ZZB). We obtain the WWB and ZZB for the Newtonian-form of the coalescing binary waveform, and compare them with published CRB and numerical Monte-Carlo results. At large SNR, we find that the theoretical bounds are all identical and are attained by the Monte-Carlo results. As SNR gradually drops below 10, the WWB and ZZB are both found to provide increasingly tighter lower bounds than the CRB. However, at these levels of moderate SNR, there is a significant departure between all the bounds and the numerical Monte-Carlo results.