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: [email protected] > [mailto:[email protected]] 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 > > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to > https://www.febo.com/cgi-> bin/mailman/listinfo/time-nuts > and > follow the instructions there. > _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
