Total variance, an estimator of long-term frequency stability [standards]

Area of Science:

• Statistics
• Metrology
• Signal Processing

Background:

• Accurate frequency stability estimation is crucial in various scientific and engineering fields.
• Traditional methods like Allan variance have limitations in certain averaging time regimes.
• The need for improved statistical tools for time-domain frequency analysis is recognized.

Purpose of the Study:

• To introduce and evaluate total variance as a novel statistical tool for frequency stability analysis.
• To compare the performance of total variance against the standard Allan variance estimator.
• To demonstrate the utility of total variance for improved frequency stability estimates.

Main Methods:

• Development of the total variance statistical definition and properties.
• Decomposition of sample variance into components related to averaging time.
• Comparative analysis of total variance and Allan variance using theoretical properties like equivalent degrees of freedom and mean square error.

Main Results:

• Total variance provides an exact decomposition of sample variance for frequency residuals.
• It enables improved frequency stability estimates at averaging times up to one-half the test duration.
• Total variance exhibits greater equivalent degrees of freedom and lesser mean square error compared to the standard unbiased Allan variance estimator.

Conclusions:

• Total variance is a valuable statistical tool for enhancing frequency stability estimations.
• Its properties make it a superior estimator to Allan variance in specific contexts.
• The findings support the adoption of total variance in metrology and signal processing applications.