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 ith
measurement of y, then )y = yi+1
- yi. 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
