Least-squares analysis of clock frequency comparison data to deduce optimized frequency and frequency ratio values

TL;DR

This paper introduces a least-squares method for analyzing clock frequency comparison data to derive optimized frequency ratios, ensuring consistency with international standards and highlighting the importance of data correlations.

Contribution

It presents a novel least-squares adjustment procedure for clock frequency data, inspired by CODATA methods, to produce self-consistent and optimized frequency ratios.

Findings

Reproduces recommended frequency values using existing data

Demonstrates the method's effectiveness with current standards

Highlights the significance of data correlation in analysis

Abstract

A method is presented for analysing over-determined sets of clock frequency comparison data involving standards based on a number of different reference transitions. This least-squares adjustment procedure, which is based on the method used by CODATA to derive a self-consistent set of values for the fundamental physical constants, can be used to derive optimized values for the frequency ratios of all possible pairs of reference transitions. It is demonstrated to reproduce the frequency values recommended by the International Committee for Weights and Measures, when using the same input data used to derive those values. The effects of including more recently published data in the evaluation is discussed and the importance of accounting for correlations between the input data is emphasised.