Estimating the stability of N clocks with correlations

Area of Science:

• Metrology
• Atomic Clocks
• Frequency Stability Estimation

Background:

• The three-cornered hat (TCH) procedure is standard for estimating atomic clock frequency stability.
• A key assumption of TCH is the statistical independence (uncorrelation) of the clocks.
• Violating this assumption can lead to inaccurate, even negative, frequency stability estimates.

Purpose of the Study:

• To extend existing methods for analyzing correlated atomic clocks.
• To develop a mathematically consistent approach for frequency stability estimation in the presence of clock correlations.
• To apply these methods to real-world atomic clock data.

Main Methods:

• Building upon previous analyses that account for inter-clock correlations.
• Applying extended statistical methods to frequency stability estimation.
• Deriving optimal clock weighting for minimum variance combination.

Main Results:

• Developed a method for mathematically consistent frequency stability estimation with correlated atomic clocks.
• Successfully applied the extended method to atomic clock data from the U.S. Naval Observatory.
• Derived an expression for optimal clock weighting to minimize variance in correlated systems.

Conclusions:

• The standard three-cornered hat method requires careful consideration of clock correlations.
• The developed method provides reliable frequency stability estimates even when clocks are correlated.
• The derived clock weighting scheme optimizes combined clock performance under correlation.