# Noise spectral estimation methods and their impact on gravitational wave measurement of compact binary mergers

## TL;DR

This paper compares two noise spectral estimation methods for gravitational wave detectors, highlighting that fitting the power spectrum with splines and Lorentzians yields more reliable results for parameter estimation.

## Contribution

It introduces and evaluates a new spectral estimation method using spline and Lorentzian fits, improving noise whitening accuracy in gravitational wave data analysis.

## Key findings

- Spline and Lorentzian fitting method is more reliable for noise estimation.
- Large data median Welch method is less effective when signals are present.
- Improved noise estimation enhances gravitational wave parameter accuracy.

## Abstract

Estimating the parameters of gravitational wave signals detected by ground-based detectors requires an understanding of the properties of the detectors' noise. In particular, the most commonly used likelihood function for gravitational wave data analysis assumes that the noise is Gaussian, stationary, and of known frequency-dependent variance. The variance of the colored Gaussian noise is used as a whitening filter on the data before computation of the likelihood function. In practice the noise variance is not known and it evolves over timescales of dozens of seconds to minutes. We study two methods for estimating this whitening filter for ground-based gravitational wave detectors with the goal of performing parameter estimation studies. The first method uses large amounts of data separated from the specific segment we wish to analyze and computes the power spectral density of the noise through the mean-median Welch method. The second method uses the same data segment as the parameter estimation analysis, which potentially includes a gravitational wave signal, and obtains the whitening filter through a fit of the power spectrum of the data in terms of a sum of splines and Lorentzians. We compare these two methods and argue that the latter is more reliable for gravitational wave parameter estimation.