[time-nuts] ADEV vs. OADEV

[Magnus Danielson]

Hej Bruce,

> 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.

I agree. Other sources is much more careful on this point. SP1065 gives 
a great overview, but should not be mistaken as a definite reference in 
all aspects.

Bregni for instance presents the definitions in one place (Chapter 5) 
and estimators in another (Chapter 7). G.810 does the same for instance.

It should be clear that the definition of Allan variance is actually not 
on two samples of frequency, they are measures of two average frequency 
measures, which implies an tau-long integral over v(t) for two 
end-to-end ranges. Using samples of frequency or samples of time is 
doing an estimation or approximation to the actual definition. I don't 
recall which paper wrote it, but it was pointed out that the average 
line over the y is often missed, but it you look in early papers these 
are found and uses, such as the tn121 paper i TN1337.

It takes the reading of alot of papers and books to really make the 
picture stand out as subtle points is pointed out here and there. I just 
learned that J. J. Snyder is to take credit for the improved overlapped 
Allan variance estimator and that this became an inspiration for the 
modified Allan variation.

> For example using the terminology of SP1065:
> 
> Classical AVAR
> Overlapped AVAR
> TOTVAR
> MTOT
> 
> are all estimators of the Allan variance.

You missed Theo1, just read the beginning of 5.2.15 and the info-box 
there. Then the followup is TheoH in 5.2.16.

> They all have the same Expectation value but the confidence limits for
> each of these estimators are different.
> 
> MVAR
> MTOT
> 
> 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.

Agree.

In the end, while I have only very quickly browsed through the material 
and picked up some new, I feel it is time to read it through properly 
again. I think I have learned a few finer points in the last days and 
when seeing it with fresh eyes I think I will appreciate many of the 
comments better.

Cheers,
Magnus