[time-nuts] Rb as source for ADEV?

[Magnus Danielson]

On 07/02/14 04:22, Tom Van Baak wrote:
>> I never knew about these different versions of ADEV.
>> Can you point me to any reference?
>>
>> Rick
>
> Hi Rick,
>
> There are a couple of separate issues regarding ADEV.
>
> 1)
> In old literature ADEV was computed using adjacent segments of data. This is about all you could do with a HP 5360A computing counter. Once real computers got into the game, it was possible to use the "overlapping" version of ADEV, which "milks" more information from the data set. You can see the two different formulas for computing it at: http://www.wriley.com/paper2ht.htm
>
> See calc_adev() source code at: http://leapsecond.com/tools/adev_lib.c
>
> Really, the only thing the overlapping version does is use a "stride" of 1 instead of tau. This is possible when you have the whole data set in memory. The more primitive back-to-back ADEV could be computed as a summing sum, requiring no data storage at all (typical of 60's and 70's instruments).

If you read up, you discover that the overlapping trick only came in as 
an inspiration for ADEV with a pair of articles from J.J. Snyder which 
took inspiration from ways to get laser frequency estimates quickly. The 
overlapping technique came to be introduced alongside the tau 
pre-filtering for the modified Allan Deviation, as can be found in the 
original MDEV article.

> 2)
> Regardless of back-to-back or overlap, there's also the question of how many points to plot. Again, in the early days, because both computation and plotting was very time consuming, people tended to plot only a few points per decade. Maybe tau 1,10,100,1000 or 1,2,5,10,20,50, or 1,2,4,8,16,32, etc. To make it look more like a graph they would connect the dots with lines (and guessing). These days, calculating ADEV is so fast there's no need to even draw the lines; just compute ADEV for every tau you can imagine and the dots connect themselves due to their density.
>
> Stable32 has an "all tau" option in which case ADEV is computed for every possible tau. E.g., 1 to 100,000. However, it turns out this is overkill. Not so much for small tau (say 1 to 100), but once you get up to the thousands or tens of thousands there's usually no significant difference between using tau N and N+1. And it can actually take a lot of time to compute ADEV hundreds of thousands of times. So we are now in the era of "many tau" which computes lots of tau *per decade*. Think of it as a logarithmic sweep of tau instead of a linear sweep. For large data sets this is orders of magnitude faster than "all tau", yet it still fills in all the gaps in the plot with real points, not extrapolated lines. Note that Timelab does "many tau" by default.
>
> 3)
> And the third issue is, of course, what child in the ADEV family to use: ADEV, MDEV, TDEV, HDEV, etc.

Actually, it's not that simple. You actually have a wider palette of 
selections to choose from:

Frequency or time stability - ADEV vs TDEV - a scaling issue

Pre-filtering - ADEV vs MDEV - a tau-averaging filter allows better 
noise separation

Derivate processing - ADEV vs HDEV - 2nd vs 3rd phase derivate, higher 
derivates will surpress more systematic frequency drift components

Degrees of Freedom processing - non-overlapping, overlapping, total, theo

In principle you can choose algorithm from the full combinatorial 
matrix, but all the slots isn't filled in, as there is no point in doing 
non-overlapping MDEV and TDEVs, since overlapping is so simple and gives 
so good performance. There is no point in doing non-filtered TDEV, as 
MDEV gives better analysis than ADEV. The scaling is trivial for both. 
This is to show that the progress of development in these various fields 
have been on-going. TOTAL and Theo is better in general, but might be 
more processing than it is worth.

I've tried to convey this on the ADEV wikipedia page, but I'm sure it 
can be improved.

Dr. Allan makes the point that one should be using MDEV rather than 
ADEV, as MDEV was what he wanted ADEV to do, but could not originally, 
so he was so happy to fix it. I agree with his motivation and analysis.

Anyway, what is the problem you are trying to solve? The "correct" 
answer depends from case to case.

Cheers,
Magnus