Magnus Danielson magnus at rubidium.dyndns.org
Thu Jan 22 06:53:11 EST 2009

```Ulrich,

Ulrich Bangert skrev:
> Magnus,
>
>> Actually, what you describe is the estimator formulas rather than
>> definition. This is also targeting the fine point that I am trying to
>> make. It's not about the basic definition, but accepted convention to
>> denote the estimators.
>
> I still do not understand the fine point! A estimator might have this
> property and that property and may perform this task good and another
> task bad, but at the basics we have a formula and if the formula is new
> or different from prior art then the thing needs an name of its own.

This part we agree on, however, you fail to see that what I try to point
out is that you seems to have the wrong reference to start with. What I
am trying to say is that it seems that ADEV is being used to identify a
different estimator than I have in my old material, including the
articles collected in NIST TN1337, for instance "Time and Frequency
(Time-Domain) Characterization, Estimation, and Prediction of Precision
Clocks and Oscillators" by David W. Allan.
http://tf.nist.gov/timefreq/general/tn1337/Tn121.pdf
See page 4 and formulas 8 and 9. These are overlapping.

> In this sense the summation over square(y(i+1)-y(i)) is called the base of
> the "Allan variance/deviation" just for historical reasons. So the name
> is "Allen deviation" and it is defined by its formula.

A further reference would be the IEEE standard found in

http://tf.nist.gov/timefreq/general/tn1337/Tn139.pdf

This is also overlapping (from page 2):

N-2m
___
2              1       \                        2
sigma  (tau) = -----------   >   (x     - 2x    + x )
y                   2  /___   i+2m     i+m    i
2(N-2m)tau   i = 1

a non-interleaved variant would have to be written as (assuming that m
divides N):

N
- - 2
m
___
m        \                              2
------------   >   (x       - 2x       + x  )
2   /___   (i+2)m     (i+1)m    im
2(N-2m)tau    i = 1

and these obviously isn't the same, the later form skips over samples
not being a multiple of m.

Also, it is still overlapping in the sense that samples is being re-used.

>> Disagree. The estimator formulation that is classically used includes
>> these "missed" tau0 steps that you claim that OAVAR/OADEV
>> includes. This is my point. Somewhere along the line the established
>> became the OADEV estimator and another estimator took the ADEV place.
>> This is what I oppose without a more detailed look at things.
>
> The OAVAR/OADEV has this name of its own BECAUSE it includes the
> summands that are missed by the original AVAR/ADEV so its needs an name
> of its own.

I deeply disagree, see my reference to early papers (I agree not
original). Also, the standardised form is overlapping.

This is the reason for me to react.

>> Somewhere along the line the established ADEV estimator became the
>
> If you had said: "The currently established estimator for oscillator
> stability is the OADEV estimator" I would have perfectly agreed.

Well, that part was never what we disagreed on IMHO.

> However, ADEV does already point to a different thing, so to say "Today
> we call ADEV what was formerly called OADEV and what was formerly called
> ADEV now is also called different" is not excused with a certain
> sloppiness in language but simply wrong use of terms. Exactly this is
> the point why I said that the discussion is dangerous. This is not a
> change in paradigm this is a case of inaccurate use of scientifical
> terms.

Well, if we were doing a shift in interpretation I fully agree with you,
but what I reacted on was due to a shift in interpretation as I
experienced it and when looking at the old reference material (altought
I have not had the time for an extensive search that I would feel
confident with). The issue was that I detected the dangerous shift and I
wanted to bring it up to bring it back on tracks, or at least learn
something useful.

I really kindly ask you or anyone else to bring forward articles
describing the non-overlapping ADEV and help plotting out the issues.
What has become standardised (and thus assumed accepted) as the ADEV
estimator is overlappping unless you can point out that I have made a
very deep misunderstanding of all those papers, in which case I would be
happy to be corrected.

Cheers,
Magnus

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