[time-nuts] ADEV vs. OADEV

Ulrich Bangert df6jb at ulrich-bangert.de
Thu Jan 22 10:50:19 UTC 2009


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. 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.  

> 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
ADEV estimator 
> 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.

>Somewhere along the line the established ADEV estimator became the
OADEV estimator

If you had said: "The currently established estimator for oscillator
stability is the OADEV estimator" I would have perfectly agreed.
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.

Best regards
Ulrich



> -----Ursprungliche Nachricht-----
> Von: time-nuts-bounces at febo.com 
> [mailto:time-nuts-bounces at febo.com] Im Auftrag von Magnus Danielson
> Gesendet: Donnerstag, 22. Januar 2009 10:57
> An: Discussion of precise time and frequency measurement
> Betreff: Re: [time-nuts] ADEV vs. OADEV
> 
> 
> Ulrich,
> 
> Ulrich Bangert skrev:
> > Magnus,
> > 
> > I am aware that you know a lot about these things. Nevertheless I 
> > believe you are starting a most dangerous discussion in the 
> sense that 
> > you put some terms into question of which I believed that they have 
> > well been established.
> 
> I have only recently seen the OADEV being used where as I have seen 
> countless articles on calculations of these without 
> encountering them, 
> so from my standpoint OADEV is not well established, which is why I 
> raised the question in order to "shake the tree" to see what 
> fruits that 
> I have missed.
> 
> > For that reason let me test where we agree and where
> > not:
> > 
> > Mr. Allan decided that for his new statistical measure the 
> summation 
> > shall run over
> > 
> > square(y(i+1)-y(i))
> > 
> > for frequency data and over
> > 
> > square(x(i+2)-2*x(i+1)+(xi))
> > 
> > for phase data. Both in contrast to the standard deviation 
> where the 
> > summation runs over squares of distances from the mean. This new 
> > variance was called "Allan variance" and its square root "Allan 
> > deviation" to honor Mr. Allan for his work. This variance/deviation 
> > has a certain "overlapping aspect" since a single y(i) or 
> x(i) appears 
> > in multiple terms of the summation. Agreed?
> 
> Yes, yes....
> 
> 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.
> 
> > Both terms require that the elements with subsequent indices are 
> > spaced apart at the "Tau" for wich the computation shall be done. 
> > Considered a number of phase measurements spaced 1 s apart then the 
> > computation will run over
> > 
> > square(x(i+2)-2*x(i+1)+(xi))
> > 
> > for Tau = 1 s. If you are going to compute for Tau = 2 s 
> from the SAME 
> > data set you will have to use the "original" samples
> > 
> > square(x(5)-2*x(3)+x(1))
> > 
> > for the first summand and
> > 
> > square(x(7)-2*x(5)+x(3))
> > 
> > for the second summand and
> > 
> > square(x(9)-2*x(7)+x(5))
> > 
> > for the third summand and so on. All indices are incremented by two 
> > between neighbour summands because the next summand is 2 s (or two 
> > original samples) apart from the current summand. Agreed?
> 
> Yes, yes...
> 
> > As we notice the summation leaves out a number of summands 
> where the 
> > elements are also spaced 2 s apart, for example
> > 
> > square(x(6)-2*x(4)+x(2))
> > 
> > or
> > 
> > square(x(8)-2*x(6)+x(4))
> > 
> > If we use these additional terms in the summation the number of 
> > summands increases a lot and improves the confidence 
> interval of the 
> > estimation, even though the added summands are NOT completely 
> > statistical independend from the original ones and therefore this 
> > measure shall be clearly distincted from the original Allan 
> > variance/deviation. The summation over the original terms plus the 
> > added terms delivers the "Overlapping Allan variance/deviation" in 
> > conjunction with a suitable normation factor. Agreed?
> 
> 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 ADEV estimator 
> became the OADEV estimator and another estimator took the ADEV place. 
> This is what I oppose without a more detailed look at things.
> 
> I agree that it changes the statistical properties in terms of 
> confidence interval, but it also change the frequency dependence. The 
> analysis on frequency dependency needs to be redone as I 
> suspect they do 
> not always agree.
> 
> Cheers,
> Magnus
> 
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