[time-nuts] A philosophy of science view on the tight pll discussion

Steve Rooke sar10538 at gmail.com
Sat Jun 5 11:19:48 UTC 2010

So, at best, it's an estimate.


On 5 June 2010 23:07, Magnus Danielson <magnus at rubidium.dyndns.org> 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
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Steve Rooke - ZL3TUV & G8KVD
The only reason for time is so that everything doesn't happen at once.
- Einstein

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