# KLTS: A rigorous method to compute the confidence intervals for the Three-Cornered Hat and for Groslambert Covariance

## TL;DR

This paper introduces KLTS, a Bayesian method that computes reliable confidence intervals for clock stability estimators, addressing limitations of existing methods at large integration times.

## Contribution

The paper presents KLTS, a novel Bayesian approach that provides accurate confidence intervals for Three-Cornered Hat and Groslambert Covariance estimators, even with limited degrees of freedom.

## Key findings

- KLTS produces reliable confidence intervals verified by extensive simulations.
- The method ensures positive stability estimates across all conditions.
- Experimental results demonstrate practical applicability of KLTS.

## Abstract

The three-cornered hat / Groslambert Covariance methods are widely used to estimate the stability of each individual clock in a set of three, but no method gives reliable confidence intervals for large integration times. We propose a new KLTS (Karhunen-Lo\`eve Tansform using Sufficient statistics) method which uses these estimators to take into account the statistics of all the measurements between the pairs of clocks in a Bayesian way. The resulting Cumulative Density Function (CDF) yields confidence intervals for each clock AVAR. This CDF provides also a stability estimator which is always positive. Checked by massive Monte-Carlo simulations, KLTS proves to be perfectly reliable even for one degree of freedom. An example of experimental measurement is given.