The dynamic Allan variance

We present and discuss the dynamic Allan variance, a measure of the time-varying stability of an atomic clock. First, the dynamic Allan variance is mathematically defined, then its behavior is extensively tested on simulated and experimental data. The results prove the validity and the effectiveness of the proposed new tool.

[1]  D. W. Allan,et al.  Statistics of atomic frequency standards , 1966 .

[2]  Chak Ming Chie,et al.  Theory of oscillator instability based upon structure functions , 1976, Proceedings of the IEEE.

[3]  P. Kartaschoff,et al.  Frequency and time , 1978 .

[4]  D. W. Allan,et al.  Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators , 1987, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[5]  D. W. Allan,et al.  Should the classical variance be used as a basic measure in standards metrology? , 1987, IEEE Transactions on Instrumentation and Measurement.

[6]  Eric Lantz,et al.  Oscillator noise analysis: multivariance measurement , 1993 .

[7]  Richard L. Sydnor.  The Selection and Use of Precise Frequency and Time Systems , 1996 .

[8]  D. Percival,et al.  Total variance, an estimator of long-term frequency stability [standards] , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[9]  David A. Howe,et al.  A total estimator of the Hadamard function used for GPS operations , 2000 .

[10]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[11]  Lorenzo Galleani,et al.  The characterization of clock behavior with the dynamic Allan variance , 2003, IEEE International Frequency Control Symposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum, 2003. Proceedings of the 2003.

[12]  P. Tavella,et al.  Tracking nonstationarities in clock noises using the dynamic allan variance , 2005, Proceedings of the 2005 IEEE International Frequency Control Symposium and Exposition, 2005..

[13]  Mihran Miranian,et al.  An Ensemble of Ultra-Stable Quartz Oscillators to Improve Spacecraft Onboard Frequency Stability , 2006 .

[14]  L. Galleani,et al.  Interpretation of the dynamic Allan variance of nonstationary clock data , 2007, 2007 IEEE International Frequency Control Symposium Joint with the 21st European Frequency and Time Forum.

[15]  P. Tavella,et al.  Implementation of the dynamic Allan variance for the Galileo System Test Bed V2 , 2007, 2007 IEEE International Frequency Control Symposium Joint with the 21st European Frequency and Time Forum.

[16]  Lorenzo Galleani,et al.  Detection of Anomalies in the Behavior of Atomic Clocks , 2007, IEEE Transactions on Instrumentation and Measurement.