So, at best, it's an estimate. Steve
On 5 June 2010 23:07, Magnus Danielson <[email protected]> wrote: > On 06/03/2010 02:15 PM, Ulrich Bangert wrote: >> >> Gentlemen, >> >> the discussion between Bruce and Warren concerning Warren's implementation >> of NIST's "Tight PLL Method" has caused quite a stir in our group. >> >> My scientifical knowledge about the discussed topic is so much inferior >> compared to Bruce's one that I don't have the heart to enter a >> contribution >> to the discussion itself. It may however be helpful to have a look at the >> discussion from a "philosophy of science" point of view. >> >> The most basic form of logic is the propositional logic. > > I think even attempting propositional logic has a basic flaw, namely can the > tentative goal be reached at all? > > In this case, can we get a "True Allan variance" measure? > > The answer is simply no. We can't get it. We can get close to it thought. > > First of all, the definition for Allan variance comes with a set of > assumptions. It assumes that dead-time is zero. If it is very near zero > (i.e. just a fraction of tau0), you will get values very near the true Allan > variance, and it may be handled using either the B2 or B3 bias function. The > bias functions was invented to translate a non-zero dead-time measurement > into a zero-dead-time measurement. To do this, the dominant noise-form for > the intended tau needs to be identified, this is where reading NIST SP1065 > becomes useful and actually very simple to implement. > > Second, the bandwidth of the measurement system needs to known and > documented with the measurement, as the WPM and FPM noise forms will have > Allan variance measures depending on the system bandwidth. > > Third, the bandwidth limit itself is assumed to be far away from the taus of > interest, or else the traditional formulas for various noiseforms is not > valid. > > Fourth, the slope of the system bandwidth is assumed to be brick-wall. > Again, for WPM and FPM noises, this will have a noticeable effect, but the > other noise forms will also be affected if they are too close the limit. The > theoretical formulas often replicated for the noise types does not include > include the slope tail, but is simply integrated over f from 0 to f_H and > then ignores the slope. > > Fifth, the definition assumes an infinit average from minus infinity to plus > infinity. We can't wait that long and we just wasn't there to setup the > measurement to start with, we have to revert to statistical estimators. > Statistical estimators can then be biased (scale or offset values) and have > different efficiency in using the available data to come arbitrarilly close > to the true value, without reaching it. > > Sixth, the definition assumes a system of no systematic drift, environmental > effects and such which will limit the measurement as it is intended to be > used for noise only. > > Seventh, all measurements includes imperfections such as trigger jitter, > stability of reference(s), stability of circuit, non-linearity of circuit, > cross-talk, dependence on temperature, resolution, etc. etc. > > ... and as you probably got by now, I can keep going on. > > So, the basic assumption of being able to get the "True" value is false, so > we have to revert to second best... close enought approximation. If you look > into the roots of Allan variance you will discover that it forms a tentative > base-case for a number of measurements, with many strings attached to it. > Additional details have been worked out over the years. The field is complex > and diversed. > > I think one has to be humble when relating to "True Allan variance" in that > there will always be flaws in the data one has collected and the methods one > is using. One needs to be open-minded to see that regardless of how I > collect it, I need to be able to re-evaluate it, compare it and essentially > acknowledge "that it is to the best of my current understanding". In this > hunt for the unobtainable, trying to remove error sources becomes a matter > of art. > > Cross-correlation gains is among the tricks in the hat we pull out to get > below some limits. > > 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. > -- Steve Rooke - ZL3TUV & G8KVD The only reason for time is so that everything doesn't happen at once. - Einstein _______________________________________________ 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.
