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

Total variance is a statistical tool developed for improved estimates of frequency stability at averaging times up to one-half the test duration. As a descriptive statistic, total variance performs an exact decomposition of the sample variance of the frequency residuals into components associated with increasing averaging times. As an estimator of Allan variance, total variance has greater equivalent degrees of freedom and lesser mean square error than the standard unbiased estimator has.

[1]  David A. Howe,et al.  Properties of Signal Sources and Measurement Methods , 1981 .

[2]  Charles A. Greenhall,et al.  A Structure Function Representation Theorem with Applications to Frequency Stability Estimation , 1983, IEEE Transactions on Instrumentation and Measurement.

[3]  Kazuyuki Yoshimura,et al.  Degree of Freedom of the Two-Sample Variance Estimates in the Continuous Sampling , 1989 .

[4]  C. Greenhall.  Recipes for degrees of freedom of frequency stability estimators , 1991 .

[5]  D. B. Percival,et al.  Characterization of frequency stability: frequency-domain estimation of stability measures , 1991, Proc. IEEE.

[6]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[7]  Marc A. Weiss,et al.  Confidence of the three-point estimator of frequency drift , 1993 .

[8]  D. W. Martin,et al.  1995 IEEE INTERNATIONAL FREQUENCY CONTROL SYMPOSIUM , 1993 .

[9]  Donald B. Percival,et al.  Wavelet variance, Allan variance, and leakage , 1995 .

[10]  David A. Howe,et al.  An extension of the Allan variance with increased confidence at long term , 1995, Proceedings of the 1995 IEEE International Frequency Control Symposium (49th Annual Symposium).

[11]  D. Howe,et al.  Circular representation of infinitely extended sequences , 1995, Proceedings of the 1995 IEEE International Frequency Control Symposium (49th Annual Symposium).

[12]  D. Howe,et al.  Effect of drift on TOTALDEV , 1996, Proceedings of 1996 IEEE International Frequency Control Symposium.

[13]  Marc A. Weiss,et al.  A Simple Algorithm for Approximating Confidence on the Modified Allan Variance and the Time Variance , 1996 .

[14]  On wavelet variance , 1997, Proceedings of International Frequency Control Symposium.

[15]  Donald B. Percival,et al.  Total Variance as an Exact Analysis of the Sample Variance , 1997 .

[16]  D. Percival,et al.  Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets , 1997 .

[17]  C. A. Greenhall,et al.  A frequency-drift estimator and its removal from modified Allan variance , 1997, Proceedings of International Frequency Control Symposium.

[18]  A..  Total Variance : a Progress Report on a New Frequency Stability Characterization * , .