Predicting Long-Term Stability of Precise Oscillators under Influence of Frequency Drift

Area of Science:

• Metrology and Measurement Science
• Signal Processing
• Optimization Theory

Background:

• High-performance oscillators, such as atomic clocks, are critical components in diverse fields including industry, finance, and scientific research.
• Accurate estimation and prediction of long-term frequency stability are essential for maintaining the performance and reliability of these oscillators.

Purpose of the Study:

• To develop and validate advanced methods for estimating and predicting the long-term frequency stability of high-performance oscillators.
• To address the challenge of frequency drift and its impact on stability metrics.
• To improve the computational efficiency of stability analysis techniques.

Main Methods:

• Application of convex optimization techniques and compressive sensing for stability estimation and prediction.
• Formulation of the influence of frequency drift on Allan and modified Allan variances.
• Derivation of expressions for the expectation and variance of discrete-time Hadamard variance, along with methods to reduce computational complexity.

Main Results:

• The proposed methods effectively incorporate frequency drift into stability analysis.
• New expressions for discrete-time Hadamard variance and associated computational efficiency improvements were developed.
• Validation using GPS precise clock data demonstrated accurate prediction of one-week frequency stability from 14-day measurements.

Conclusions:

• The study presents a robust framework for predicting long-term frequency stability in high-performance oscillators.
• The developed techniques offer improved accuracy and computational efficiency compared to traditional methods.
• The findings have significant implications for the reliable operation and maintenance of critical timing systems.