[time-nuts] ADEV vs. OADEV

Magnus Danielson magnus at rubidium.dyndns.org
Thu Jan 22 21:18:38 EST 2009

Tom Van Baak skrev:
> Yes, it is interesting that SP1065 uses words like:
>   "original Allan" (page 2, 3, 14)
>   "classic Allan variance" (page 11)
>   "normal Allan variance" (page 16)
> as a way to distinguish the non- from the overlapping version.
> We could throw in "traditional", "simple", "back-to-back", "plain".

Depending on the context of course.

> I agree with the author (W.Riley) that these days ADEV is
> moving towards being interpreted, and more frequently
> implemented, as the overlapping variety, but that might take
> a generation to sink in.

Maybe. The J.J. Snyder article is from 1980 where as the Allan deviation 
is from 1966. It's only about half-a-generation. Maybe about the age 
difference of us two...

> I mean, even his own Stable32 program calls the default
> 2-sample variance "Allan" and if you want the overlapped
> version you have to click on "Overlapping Allan".

This could indicate where he is on the issue, but does not really 
resolve the question.

> So you see why that Allan tool of mine labels the columns
> adev and oadev? At least there's no ambiguity that way.

That I agree with, in your context you certainly avoided ambiguity.

> I should also point out that not all systems can calculate
> overlapping Allan statistics. Some realtime analyzers, even
> the fancy TSC boxes for example, cannot do full overlapping
> (because you need access to the entire data set for that).
> So plain adev is not dead yet.

Actually... no. I have looked at this problem and you can calculate the 
overlapping Allan variance in real time with only the 2m tau of historic 
x values in memory. It is fairly trivial to implement out of the 
definition. You don't need the full data-set. However, you would need 
multiple accumulators for different choices of m. I can see how this 
might not is imminently apparent, but given the clues given I think it 
will become visible.

The trickier part is to do drift rate compensation without having access 
to the full dataset. For Allan variance this is possible with a few 
tricks out of the statistics book.

Using such an approach, you could see your AVAR/ADEV develop as the time 
series is consumed and be able to see how it stabilizes as you measure 
more and more. I think it is a rather pleasing approach.

What I really need to learn is to calculate the confidence intervals. It 
keep nagging me all the time.


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