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.
