Allan Variance meaning?

[Zucca]

I never understood those graphs:



I went in wikipedia and understood nothing then in google and it was difficult to make some progress.

I finally found this:

http://home.engineering.iastate.edu/~shermanp/AERE432/lectures/Rate%20Gyros/Allan%20variance.pdf

some interesting quotes:

Allan variance and its variants have proven useful outside the scope of timekeeping
and are a set of improved statistical tools to use whenever the noise processes are not unconditionally stable, thus a
derivative exists.

An Allan deviation of 1.3×10−9 at observation time 1 s (i.e. τ = 1 s) should be interpreted as there being an instability
in frequency between two observations a second apart with a relative root mean square (RMS) value of 1.3×10−9.
For a 10-MHz clock, this would be equivalent to 13 mHz RMS movement. If the phase stability of an oscillator is
needed then the time deviation variants should be consulted and used.

If someone has better stuff to feed me please help.
Still baby steps into something I never saw before.

[unitedatoms]

I have no clue either. But your question is about sources of definitions. There is a page from man himself.

http://www.allanstime.com/AllanVariance/index.html

Edit: I followed the example in the article provided by author. It looks like Allan deviation of clock with error of 1.000 sec per day is 0.707 sec.

My personal understanding is: Allan Deviation is sort of RMS "energy" of noise which can be computed from just 2 samples.

Comment about charts: It looks like something being converged to single deviation value over longer observation. Which possibly is the purpose of Allan Deviation: to have the method of averaging which converges to some const value.

[edpalmer42]

AFAIK, oscillator aging is the biggest reason that ADEV was created in the first place.  Standard Deviation has been around forever, but when they tried to apply it to electronic oscillators they had problems.  Since the oscillators age and drift the calculations run into trouble since they assume that the only thing affecting the measurements are random variations.  ADEV is designed to accomodate aging without ending up with nasty things like zeros or infinities.  Aging will be very obvious in an ADEV graph, but it won't break the calculations.

Ed

[unitedatoms]

@edpalmer42: Oh I understood now. Standard vs Allan Deviations is like INL to DNL chart of ADC/DAC accuracies.

[Zucca]

My personal understanding is: Allan Deviation is sort of RMS "energy" of noise which can be computed from just 2 samples.

Yes, but somehow the ADEV take in account the observation time with no samples.
The lower the better is also a very very basic concept I understood.

[thinkfat]

My personal understanding is: Allan Deviation is sort of RMS "energy" of noise which can be computed from just 2 samples.

Yes, but somehow the ADEV take in account the observation time with no samples.
The lower the better is also a very very basic concept I understood.

Allen Deviation gives you a measure for stability of an input depending on the intervals for which you observe it.

For example, if you measure an oscillator now and in 1 second, the ADEV chart gives you the deviation you can expect between these two measurements.

Practical example: You evaluate a clock source for a counter that has a gate time of 10s. The ADEV chart of the clock source at Tau=10s gives you an idea of how stable your timer display will be, i.e. how many usable digits you can expect. At Tau=86400 you'll see the daily aging and so forth.

[Kleinstein]

The noise of real instruments is not necessary white. So the variations depend on the time in between. Usually 1/f type noise causes additional variations for measurements that a further apart. With only white noise the modified Allan deviation plot as shown in the initial post will show the 1/sqrt(tau) curve, about seen for the 344461 for a large part.

The Allan deviation is one way to look at different noise contributions beyond just white noise.
The curve is similar (AFAIK slightly smoothed out) to a noise spectrum plotted over 1/frequency. So the maximum at 50 seconds corresponds to extra noise (or other background) in the 0.020 Hz range.

[Zucca]

The curve is similar (AFAIK slightly smoothed out) to a noise spectrum plotted over 1/frequency. So the maximum at 50 seconds corresponds to extra noise (or other background) in the 0.020 Hz range.

Thanks Kleinstein, so the time axis could be interpreted as a 1/f, kind of frequency axis. Interesting.