On 15/08/11 18:43, Tom Van Baak wrote:
Correct. Some ADEV plots conveniently include error bars so
the effect of sample count on confidence is in your face. The
TSC 5110 does this. See for example:
http://leapsecond.com/pages/gpsdo/log35824v.gif
http://leapsecond.com/pages/gpsdo/log35825v.gif
There are also a number of modern variants on regular old Allan
deviation that improve confidence even given the same sample
count. In some cases the trade-off here is computation time.
I've spent some time in the Allan deviation article to numerical freedom
and confidence intervals. Also, today can Allan deviation be considered
more of a statistical scale rather than a particular algorithm. Already
within the Allan deviation there are some algorithmic differences, but
Hadamard, Total and Theo algorithms bring in different approaches on the
same scale, with the same statistical bias properties but with improved
statistical confidence intervals.
It is highly educating to see the realtime updates of TimeLab for
instance as it gathers more data. You can see how the upper end swings
wildly as data comes in, but for a particular tau the amplitude of the
swing lowers and becomes more and more subtle. This is the result of the
statistical properties of degrees of freedom and the effect on
confidence intervals in action.
The algorithmic advances is about to give as tight confidence interval
as possible for as short measurement time as possible, and the basic
trick is to use overlapping estimations in combination with "over the
edge" analysis. The Total analysis mirrors the data-sequence around the
edge to create a three-times longer sequence, but to avoid biases the
sequence is frequency corrected first, or else the unwrapping would
introduce false systematic noise. This could be due to low-frequency
noise or systematic effects of lower frequency than the sequence allow
for analysis, since it is a finite sequence of data... a key limitation
which is easilly forgot. The noise isn't white for longer times... which
is what causes us to go into the statistical predictor efforts of Allan
deviation and friends.
No, this isn't an easy topic, it took decades to learn and develop for
the professional researchers... and the work keeps progressing. It is
also a re-occurring discussion here.
Hopefully the Allan deviation article can get you up to speed...
Cheers,
Magnus
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