KLTS: A Rigorous Method to Compute the Confidence Intervals for the Three-Cornered Hat and for Groslambert Covariance

Area of Science:

• Metrology
• Timekeeping
• Statistical Analysis

Background:

• Existing three-cornered hat/Groslambert Covariance (GCov) methods estimate clock stability but lack reliable confidence intervals for extended integration periods.
• Accurate estimation of clock stability and its confidence intervals is crucial for high-precision timekeeping applications.

Purpose of the Study:

• To introduce a novel Karhunen-Loève Transform using Sufficient statistics (KLTS) method for estimating clock stability.
• To provide reliable confidence intervals for clock Allan variance (AVAR) even at large integration times.
• To develop a stability estimator that is inherently positive.

Main Methods:

• The KLTS method employs a Bayesian approach, integrating statistics from all pairwise clock measurements.
• It utilizes estimators from the three-cornered hat/Groslambert Covariance (GCov) methods.
• A cumulative density function (CDF) is derived to generate confidence intervals for AVAR.

Main Results:

• The KLTS method successfully yields confidence intervals for each clock's Allan variance (AVAR).
• The derived CDF provides a stability estimator that is consistently positive.
• Massive Monte Carlo simulations confirm the reliability of KLTS, even with one degree of freedom.

Conclusions:

• The KLTS method offers a significant improvement over existing techniques for estimating clock stability and confidence intervals.
• It provides a robust and reliable tool for analyzing clock performance, particularly at large integration times.
• Experimental validation demonstrates the practical applicability of the KLTS method.