A Simple Algorithm for Approximating Confidence on the Modified Allan Variance and the Time Variance

Abstract : An approximating algorithm for computing equivalent degrees of freedom of the modified Allan variance and its square root, the modified Allan deviation (MVAR and MDEV), and the time variance and time deviation (TVAR and TDEV) is presented, along with an algorithm for approximating the inverse chi-squared distribution. These two algorithms allow relatively simple computations of confidence intervals on MDEV and TDEV, the latter currently used as a standard in the telecommunications industry. These algorithms enable users to present variance with confidence intervals corresponding to any useful probability for most data lengths and noise types.

[1]  M. A. Weiss,et al.  A frequency-domain view of time-domain characterization of clocks and time and frequency distribution systems , 1991, Proceedings of the 45th Annual Symposium on Frequency Control 1991.

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

[3]  R. A. Fox,et al.  Introduction to Mathematical Statistics , 1947 .

[4]  C. A. Greenhall,et al.  A shortcut for computing the modified Allan variance , 1992, Proceedings of the 1992 IEEE Frequency Control Symposium.

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

[6]  D. W. Allan,et al.  A Modified "Allan Variance" with Increased Oscillator Characterization Ability , 1981 .

[7]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[8]  T. Walter,et al.  Characterizing frequency stability: a continuous power-law model with discrete sampling , 1994 .

[9]  G. Reinsel,et al.  Introduction to Mathematical Statistics (4th ed.). , 1980 .

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

[11]  C. Greenhall.  Estimating the modified Allan variance , 1995, Proceedings of the 1995 IEEE International Frequency Control Symposium (49th Annual Symposium).

[12]  C. A. Greenhall,et al.  Initializing a flicker-noise generator , 1986, IEEE Transactions on Instrumentation and Measurement.

[13]  Charles A Greenhall,et al.  The third-difference approach to modified Allan variance , 1997 .