[time-nuts] ADEV vs. OADEV

[Magnus Danielson]

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