Allan variance equation:

where the variance is taken on the variable y. Each value of y in a set has been averaged over
an interval J and the ys are taken in an adjacent series,
i.e. no delay between the measurements of each. The brackets <> denote the expectation
value. For a finite data set, it is taken as the average value of the quantity enclosed in the
brackets. The )y denotes the first finite difference of the
measures of y; i.e. if i denotes the i^{th} measurement of y, then )y
= y_{i+1} - y_{i}. In total, each adjacent finite difference of y is squared and
these then are averaged over the data set and divided by 2. The divide by two causes this variance
to be equal to the classical variance if the ys are taken from a random and uncorrelated set; i.e.
white noise.

The advantage of this variance over the classical variance is that it converges for most of the
commonly encountered kinds of noise, whereas the classical variance does not always converge to a
finite value. Flicker noise and random walk noise are two examples which commonly occur in clocks
and in nature where the classical variance does not converge.

For time keeping, y is taken as the normalized rate of a clock. For example, if a wrist watch
gained one second per day, then y = 1 second / 86400 seconds = 1.157e-5, and J
is equal to 1 day. Notice that y is dimensionless.

**See also**

partial list of **Independent References to the Allan Variance**

**See also**

AVAR use in radio-astronomical instrumentation - partial list of publications, compiled by
Dr. Rudolf Schieder

D.B. Sullivan, D.W. Allan, D.A. Howe, and F.L. Walls, **Characterization of Clocks and
Oscillators**, NIST Tech Note 1337, 1990. (BIN: 868)

D.W. Allan, H. Hellwig, P. Kartaschoff, J. Vanier, J. Vig, G.M.R. Winkler, and N.F. Yannoni, **Standard
Terminology for Fundamental Frequency and Time Metrology**, Proceedings of the 42nd
Annual Frequency Control Symposium, Baltimore, MD, June 1-4, 419-425, 1988. (BIN: 788)

D.W. Allan, *Statistics of Atomic Frequency Standard*, Proceedings of the
IEEE, 54, No. 2, 221-231, 1966. (BIN: 7)

D.W. Allan and J.A. Barnes, **A Modified "Allan Variance" with Increased
Oscillator Characterization Ability**, Proceedings of the 35th Annual Frequency
Control Symposium,, 470-475, 1981. (BIN: 560) {click
here for abstract}

D.W. Allan, **Should the Classical Variance Be Used as a Basic Measure in Standards
Metrology?**, IEEE Trans. on Instrumentation and Measurement, IM-36, 646-654, 1987.
(BIN: 776)

D.W. Allan, **Time and Frequency (Time-Domain) Characterization, Estimation, and
Prediction of Precision Clocks and Oscillators**, IEEE Transactions on Ultrasonics,
Ferroelectrics, and Frequency Control, UFFC-34, 647-654, 1987. (BIN: 752)

David W. Allan, Wayne Dewey; *Time-Domain Spectrum of GPS SA*; Proceedings of 1993
Institute of Navigation ION GPS-93.

D.W. Allan, M.A. Weiss and T.K. Peppler, **In Search of the Best Clock**,
IEEE Transactions on Instrumentation and Measurement, 38, 624-630, 1989. (BIN: 815)

D.W. Allan, **Millisecond Pulsar Rivals Best Atomic Clock Stability, Proceedings of the
41st Annual Symposium on Frequency Control**, Philadelphia, PA, 2-11, 1987. (BIN: 751)

David W. Allan; *The
Impact of Precise Time in Our Lives: A Historical and Futuristic Perspective Surrounding GPS*;
50th Anniversary Invited Talk at Institute of Navigation Annual Meeting, held in Colorado Springs,
Colorado; 5-7 June 1995.

D.W. Allan, **Clock
Characterization Tutorial**, Proceedings of the 15th Annual Precise Time and Time
Interval (PTTI) Applications and Planning Meeting, 1983. (BIN: 662)

F. Varnum, D.R. Brown, D.W.
Allan, and T.K. Peppler, **Comparison of Time Scales Generated with the NBS Ensembling
Algorithm**, Proceedings of the 19th Precise Time and Time Interval (PTTI) Meeting,
1987.

**MORE** . . . click here for list of publications relevant to
the Allan Variance