[time-nuts] ADEV vs. OADEV

Bruce Griffiths bruce.griffiths at xtra.co.nz
Thu Jan 22 20:03:08 EST 2009

Magnus Danielson wrote:
> Tom Van Baak skrev:
>>> One point of confusion is that AVAR(tau) should not be directly 
>>> interpreted as Allan Variance in general, it is actually already defined 
>>> and reserved to mean a chosen Allan Variance estimator. This is an 
>> Sorry if I'm jumping into this thread late, but this statement
>> confuses me.
> Feel free to join in...
>> Since when is "AVAR" not simply short-hand
>> for "Allan Variance"?
> Good question. My point being that yes... AVAR is a handy short-hand for 
> Allan Deviation, but it is also actually a standardised quantity and 
> several standards actually define it consistently as a particular 
> estimator. It's a good estimator for being of the Allan Variance family 
> and CPU-cycles should not prohibit us from using it.
> Recall that they are all estimators. I think this is a crutial point to 
> learn really. Once one has accepted that fact, then taking a look at 
> which estimator serves me the best becomes the issue of interest, not 
> "which is the right one?" which is actually an incorrect question in 
> this context.
> So, feel free to short-hand Allan Variance as AVAR, but there are 
> context in which this is going to be interpreted as being the 
> overlapping Allan variance estimator and not any other estimator, and 
> hence using that short-hand can be ambiguous. If we want an unambiguous 
> use of AVAR, do not use AVAR as short-hand for Allan Variance when using 
> other estimators than the overlapping one. Do as you please, but now you 
> are aware of the issue.
> Also, look at the NIST SP 1065 for instance, where it is clearly 
> indicated that the "original" is being superseded in most practical use 
> for the benefit of the overlapping, giving improved confidence 
> intervals. Also, Modified Allan Variance and Theo should be considered 
> as better alternatives.
> The SP 1065 should be a good read for many, as it gives a modern 
> overview and also addresses several practical implementational issues 
> such as software test-sequences etc. The TN 1337 is a more classic view 
> and collection of articles.
> So... we could argue all we want about "which is the correct Allan 
> Variance" but it doesn't really help. The original estimator is flawed. 
> the overlapping estimator improves confidence and the Theo family should 
> provide even better results.
>> Next you'll tell me SDEV isn't Standard Deviation because some
>> self-important standards organization decided otherwise.
> I could probably find a standard defining it to something completely 
> different and totally out of context which would not help.
> But the reaction is natural, but one must realize that there is not real 
> "right" here, so sometimes putting down the foot and say "this is what 
> we define it to be" is needed so that everyone at least do it according 
> to the same procedures and with known errors... until you realize that 
> you need something better and move over to some other measurement which 
> you define in a similar fashion. It's like say the meter standard. "This 
> is the meter... until we say something different".
> Cheers,
> Magnus
Hej Magnus

The major failing of SP1065 is that it doesn't explicitly make it clear
that all the quantities for which its gives formulae are merely
estimators of an underlying statistical property of the frequency source.

For example using the terminology of SP1065:

Classical AVAR
Overlapped AVAR

are all estimators of the Allan variance.
They all have the same Expectation value but the confidence limits for
each of these estimators are different.


are both estimators of the Modified Allan variance.
They both have the same Expectation value but the confidence limits for
each of these estimators are different.


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