[time-nuts] ADEV vs. OADEV
Magnus Danielson
magnus at rubidium.dyndns.org
Thu Jan 22 12:24:16 UTC 2009
Bruce Griffiths skrev:
> Ulrich. Magnus
>
> Perhaps the situation is best summarised in /NIST special Publication
> 1065/ (can be downloaded as 2220.pdf
> <http://tf.nist.gov/timefreq/general/pdf/2220.pdf> from NIST) wherein it
> is stated that ADEV, AVAR are often taken to mean the overlapped form of
> the Allan deviation at least in the US.
This is an excellent contribution to the discussion as it details the
"Original Allan variance" and "Overlapping Allan variance" and also has
a special information box detailing that AVAR and ADEV used mainly
(notice standards and much of the reference material) for the
overlapping. It also shows the inability for the 2-sample variance
(Original Allan variance) to create smooth and good curves.
That the 2-sample variance existed and was the basis for Allan variance
was know, but the overlapping formulation of the established AVAR and
ADEV terms estimators is motivated and accepted for its improved
precission was also known to me indirectly, in the sense that I saw they
where not directly equivalent but saying the same thing, then I forgot
about it until this mysterious OADEV/OAVAR came up recently.
There is however a huge difference between the 2-sample variance being
the original Allan variance and being AVAR. Here I tend to rely on
standards set by IEEE and ITU-T as they establish a defined relationship
and I suspect some wisedom was applied in the process. Which estimator
is we best serviced by to get defined as AVAR? They chose the
overlapping one and it has also been the most used in theoretical
analysis to the best of my knowledge.
The plots given in the NIST SP 1065 figure 8 is very descriptive on the
difference.
In the end, I think we must realize that there is a distinction between the
2
sigma (tau)
y
and
AVAR(tau)
The former is the Original Allan Variance where as the later is the
Overlapping Allan Variance. It is easy to confuse the two. Maybe this is
the fundamental problem and not the definitions themselfs.
Cheers,
Magnus
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