[time-nuts] Allan deviation and modified Allan deviation
magnus at rubidium.dyndns.org
Mon Feb 18 23:56:52 EST 2013
On 18/02/13 20:59, cdelect at juno.com wrote:
> Ok I've been plotting my oscillators for years using Allan Deviation.
> That way all my records can be compared easily.
> Is there any advantage to using Modified Allan Deviation?
> It seems to give a better stability plot but that just seems to be
> If I plot both ways what do the differences mean?
When the Modified Allan Deviation was introduced, two things happen:
1) It fixes the "bug" in the Allan Deviation which can't make useful
differentiation between white phase modulation and flicker phase
modulation noises. This is achieved by using a tau-long averager prior
to the Allan Deviation calculation. If you are in a region where these
noises exist, use MDEV to separate them. Dave Allan himself is eager to
push MDEV over ADEV.
2) The traditional (non-overlapping) Allan Deviation estimator has poor
usage of the samples taken. The MDEV estimator given uses the
overlapping strategy to increase (but not maximize) the use of samples,
especially for longer taus. This gives improved confidence intervals.
These steps improved the state of art processing significantly in the
early 80thies. Since then have the total and Theo strategies for even
further improved use of samples to achieve good confidence intervals.
Using the traditional non-overlapping Allan deviation estimator for the
Allan Deviation measure is throwing a lot of useful data in the trash
and suffer by bad precision or long measurement-times.
Allan Deviation is frequency drift limited in its upper end, where
linear (and higher order) drift will obscure the output and hide the
noise processes that Allan Deviation is meant to analyse. Drift is a
systematic component that needs to be taken out of the data in order for
the noise processes to be visible.
The Allan Deviation has a cousin in the Hadamard Deviation, both is
normalized to the same scale (i.e. same as RMS white frequency
modulation noise). The Hadamard beats Allan for real-time processing, as
it removes the first degree frequency drift. However, for
post-processing a better drift model can be used, so drift removal on
data prior to Allan Deviation is preferred. Then, both Allan and
Hadamard Deviations can exist in their normal and modified variation,
with the tau-long averager. For degrees of freedom treatment, you can do
non-overlapping, overlapping, TOTAL and Theo processing, where TOTAL and
Theo is the best.
There is also FFT based methods to process data, but I need to refresh
myself on that.
So, it sounds like you can do a lot more with your data without cheating.
Magnus - from LA
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