Three-Cornered Hat and Groslambert Covariance: A first attempt to assess the uncertainty domains

TL;DR

This paper addresses the lack of a rigorous method to assess uncertainties in frequency stability estimates obtained via the three-cornered hat and Groslambert Covariance methods, proposing a new approach to evaluate confidence intervals.

Contribution

It introduces a novel method to assess the uncertainty domains of frequency stability estimates, including a solution to the inverse problem for confidence interval calculation.

Findings

Method is reliable from 5 Equivalent Degrees of Freedom (EDF) and beyond.

First attempt to rigorously assess uncertainties in these stability estimates.

Provides a framework for confidence interval estimation in oscillator stability analysis.

Abstract

The three-cornered hat method and the Groslambert Covariance are very often used to estimate the frequency stability of each individual oscillator in a set of three oscillators by comparing them in pairs. However, no rigorous method to assess the uncertainties over their estimates has yet been formulated. In order to overcome this lack, this paper will first study the direct problem, i.e. the calculation of the statistics of the clock stability estimates by assuming known values of the true clock stabilities and then will propose a first attempt to solve the inverse problem, i.e. the assessment of a confidence interval over the true clock stabilities by assuming known values of the clock stability estimates. We show that this method is reliable from 5 Equivalent Degrees of Freedom (EDF) and beyond.