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The dynamic Allan variance II: a fast computational algorithm.

Lorenzo Galleani¹

¹Politecnico di Torino, Torino, Italy. galleani@polito.it

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

|December 31, 2009

Summary

A new fast algorithm significantly reduces computation time for dynamic Allan variance (DAVAR), a key metric for atomic clock stability monitoring. This advancement enables efficient analysis of long time series and supports applications with limited computational resources, like space missions.

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Area of Science:

Atomic Clock Technology
Time Series Analysis
Signal Processing

Background:

Atomic clock stability is crucial for precise timekeeping but degrades over time due to environmental and aging factors.
Monitoring atomic clock stability requires analyzing time-varying performance metrics like dynamic Allan variance (DAVAR).
Traditional DAVAR computation is computationally intensive, limiting its application with long time series or in resource-constrained environments.

Purpose of the Study:

To develop a computationally efficient algorithm for calculating dynamic Allan variance (DAVAR).
To extend the fast DAVAR algorithm to handle time series data with missing values.
To demonstrate the practical benefits of the fast algorithm for atomic clock monitoring.

Main Methods:

Development of a novel, fast algorithm for DAVAR computation.
Extension of the algorithm to incorporate methods for handling missing data points in time series.
Numerical simulations to validate the computational speed and accuracy of the proposed algorithm.

Main Results:

The fast algorithm dramatically reduces the computational time required for DAVAR calculation.
The extended algorithm effectively handles time series data containing missing values.
Simulations confirm significant performance improvements compared to traditional methods.

Conclusions:

The fast DAVAR algorithm offers a substantial improvement in computational efficiency for analyzing atomic clock stability.
The ability to handle missing data makes the algorithm more robust for real-world applications.
This advancement is particularly beneficial for monitoring numerous clocks, analyzing long data sets, and in low-power computing scenarios such as onboard spacecraft.