The Corrected Allan Variance: Stability Analysis of Frequency Measurements With Missing Data

Area of Science:

• Metrology and Precision Measurement
• Statistical Signal Processing
• Atomic Physics and Clocks

Background:

• Atomic clocks are critical for applications like Global Navigation Satellite Systems (GNSS).
• Accurate performance monitoring of atomic clocks is essential for reliable operation.
• The Allan variance is the standard statistical tool for characterizing atomic clock stability.

Purpose of the Study:

• To demonstrate the bias introduced in Allan variance when using atomic clock frequency data with missing values.
• To develop and validate a method for correcting Allan variance to mitigate bias from missing data.
• To ensure reliable performance characterization of atomic clocks even with incomplete datasets.

Main Methods:

• Theoretical analysis to prove the existence of bias in Allan variance due to missing frequency measurements.
• Development of a corrected Allan variance formula to compensate for data gaps.
• Numerical simulations to validate the effectiveness of the corrected Allan variance against common atomic clock noise models.

Main Results:

• Confirmed that missing data in frequency measurements introduces significant bias into standard Allan variance calculations.
• The proposed corrected Allan variance effectively eliminates or substantially reduces this bias.
• The corrected Allan variance accurately reflects the expected performance, comparable to using full data.

Conclusions:

• The presence of missing data can severely compromise the accuracy of atomic clock performance assessments using Allan variance.
• The developed correction method provides a robust solution for obtaining unbiased Allan variance estimates.
• This work enhances the reliability of atomic clock characterization, crucial for high-precision applications.