[time-nuts] ADEV vs. OADEV

[Bruce Griffiths]

Tom Van Baak wrote:
> 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".
>
> 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.
>
> 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".
>
> So you see why that Allan tool of mine labels the columns
> adev and oadev? At least there's no ambiguity that way.
>
> 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.
>
> /tvb
>
>
>   
Tom

Its important to realise these calculated statistics are all estimators
of the underlying Allan variance.
Thus it is important to assign unique unambiguous names  to each of them
so that some idea of their region of reasonable accuracy and perhaps
their confidence limits can be estimated.

Thus for example:
AVAR doesn't actually denote the underlying Allan variance but rather a
particular algorithm used to estimate it from the data.

OAVAR denotes another algorithm for estimating the underlying Allan
variance from the data

TOTVAR, THEO1 and THEOH denote other algorithms that can be used to
estimate the underlying Allan variance from the data.

Some of these algorithms produce biased estimates of the underlying
Allan variance so correction for such bias is usually necessary.

Bruce