Fellow time-nuts,
I thought that a small blip on the screen to alert you on historical
context was appropriate.
In 1964 NASA and IEEE held a "NASA-IEEE Symposium on Short-Term
Stability" [1] producing a nice set of articles.
This was followed a special issue of IEEE proceedings on Frequency
Stability in Feb 1966. In this the articles "Statistics of Atomic
Frequency Standards" by David W. Allan [2] summarise various M-sample
variance measures, analyses them and find them bias-related to the
2-sample variance. Further, the analysis provide proof for the
convergence problems for large M values, thus showing that the 2-sample
variance provides a base-case which every other M-sample variance can be
related to. Essentially this kills the interest in M-sample variances
and replaces it with the 2-sample variance. Similarly, for dead-time
values they can using bias functions be related to non dead-time values.
So, this unified variance of 2-sample and no dead-time is proposed as a
unified vairance later called Allan's variance or Allan variance in
todays speach.
Anyway, it is now 45 years ago since that article (and several others
worth reading). I've tried to get a summary in the Allan variance
article on Wikipedia [3]. After these articles the field has been
improved significantly by improved analysis on biases,
noise-separations, statistical certainty and improved estimators to
achieve the high statistical certainty.
[1] http://hdl.handle.net/2060/19660001092
[2] http://tf.boulder.nist.gov/general/pdf/7.pdf
[3] http://en.wikipedia.org/wiki/Allan_variance
Cheers,
Magnus
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