[time-nuts] What is the correct Allan value?

[Magnus Danielson]

On 10/29/2010 08:28 PM, WarrenS wrote:
> If it is time to come back from all the "Dead" subjects, I have a time
> nut question.
>
> What is the correct 100 sec Allan value of this low noise 10811 Osc? All
> plots are of the same OSC, just different parts of the same data run.

None of them is correct, but the Overlapping 0K-563K curve is closest to 
the real curve, if only drift is compensated for. However, for the run 
you have here, drift does not dominate so no real drift needs to be 
compensated.

What you have is typical and really shows that the statistical 
confidence bounds can be very bad for longer taus using the Allan 
variance estimator... even the overlapping one.

The relative closeness of the various curves up to about 1 second comes 
from the richness of observables, or high degree of freedom. As the tau 
becomes higher the degrees of freedom falls like a stone and the 
statistical confidence intervals just blows out.

There is two basic cures for this, more data, better estimator or better 
yet, both.

The research for better estimators is motivated by the need to improve 
the quality (confidence intervals) without having very long measurement 
series. The overlapping estimator is really the first step of 
improvement of estimator, but certainly not the last. Modern estimators 
such as the Theo variants cranks out more degrees of freedom from the 
same sequence of samples and thus will have better confidence intervals 
and this moves the point where the confidence intervals blows up to 
higher taus, but it will happen eventually.

So, of the measures you have, the full-length overlapping is the best in 
that set.

I had to read up a lot when I put some time on getting the Wikipedia 
article on Allan Variance into better shape. It was darn good exercise. 
I still have a few aspects to cover in that article, but I haven't had 
the time.

Cheers,
Magnus