[time-nuts] Some long-term data

Magnus Danielson cfmd at bredband.net
Sun Dec 24 21:43:16 EST 2006

From: John Ackermann N8UR <jra at febo.com>
Subject: Re: [time-nuts] Some long-term data
Date: Sun, 24 Dec 2006 10:51:59 -0500
Message-ID: <458EA21F.6030702 at febo.com>

> Magnus Danielson said the following on 12/23/2006 07:21 PM:
> >> Magnus Danielson said the following on 12/23/2006 05:22 PM:
> >>
> >>> Such as temperature and humidity. One of the Cesiums seemed to have a rather
> >>> large frequency offset. Did you drift-compensate your ADEV measures or not?
> >> No, I ran the ADEV in Stable32 without removing drift.  My understanding
> >> is that linear drift shouldn't affect the calculation.  I was also a
> >> little concerned whether drift removal would work very well given that
> >> both Cesiums had periods where the offset changed for quite a long
> >> period (CS1 near the end of the data, CS2 at the beginning) and I wasn't
> >> sure what impact that might have.
> > 
> > I know next to nothing about Stable32, so I don't know what that black box
> > actually is doing.
> > 
> > From a theory standpoint, it is trivial to show (I've done the exercise to
> > convince myself, but it is already covered in literature) that linear frequency
> > drift does affect the result. Time/phase offset and frequency offset cancels.
> > 
> > From a practical standpoint, linear frequency drift may or may not be small
> > enought not to interfere with the measure of the noise power. To be sure,
> > measure the drift rate.
> I think I've been sloppy in my terminology above and in other messages
> -- I meant to say, as Magnus does, that linear offset doesn't affect the
> stability measurement.  Drift such as aging certainly would.

OK. I actually had to check so I hadn't been careless to write frequency rather
than frequency drift. Fortunatly I wrote the right thing, else you would have
received a correction. The devil is in the detail, as always.

Indeed, and so will also the longer and shorter tau instabilities, but that is
what the characteristics of Allan Deviation does for us, it gives the energy to
shift over a certain time-span.

Now, I made a quick little program that process the data, here is the result:

magnus at heaven:~/febo$ ./process cs1-gps.dat
Processing cs1-gps.dat
f = -1.371312943e-13
d = -2.464638917e-19
  tau         ADEV             drift       ADEV drift corr
    600  6.669673909e-12 -1.478783350e-16  6.669673908e-12
   1200  3.834415574e-12 -9.729746560e-17  3.834415573e-12
   3000  2.262840286e-12 -7.178672646e-16  2.262840229e-12
   6000  1.321830189e-12 -2.009721443e-16  1.321830182e-12
  12000  6.871654621e-13 +4.615768463e-16  6.871653846e-13
  30000  3.721752717e-13 +6.169074858e-16  3.721750161e-13
  60000  2.376494277e-13 -1.086051407e-15  2.376481869e-13
 120000  1.702980952e-13 +2.784783011e-16  1.702979813e-13
 300000  1.549264955e-13 +1.088753918e-15  1.549245826e-13
 600000  1.401676798e-13 -3.474273795e-15  1.401461493e-13
1200000  6.799762269e-14 +2.337820108e-14  6.595761175e-14
3000000  1.010049262e-13 +1.245160039e-13  4.949623724e-14
6000000  1.550028203e-13 +2.190959040e-13  4.936266040e-15
magnus at heaven:~/febo$ ./process cs2-gps.dat
Processing cs2-gps.dat
f =  5.853529458e-13
d =  1.816049729e-19
  tau         ADEV             drift       ADEV drift corr
    600  7.508211487e-12 +1.089629837e-16  7.508211486e-12
   1200  4.527916555e-12 +1.167569587e-16  4.527916554e-12
   3000  2.722308557e-12 +1.354760348e-16  2.722308555e-12
   6000  1.721060210e-12 -4.728298124e-16  1.721060178e-12
  12000  1.035443547e-12 +1.147314746e-15  1.035443229e-12
  30000  6.178807446e-13 +3.397917058e-15  6.178760731e-13
  60000  4.117968150e-13 +7.312248617e-15  4.117643529e-13
 120000  2.667708446e-13 +9.998532864e-15  2.666771423e-13
 300000  1.831015144e-13 +2.174763258e-14  1.824546103e-13
 600000  1.607481137e-13 +3.712397851e-14  1.585902304e-13
1200000  9.695302954e-14 +7.496309428e-14  8.117978311e-14
3000000  1.780291901e-13 +2.206804427e-13  8.569984631e-14
6000000  3.223233857e-13 +4.553265537e-13  1.520624005e-14
magnus at heaven:~/febo$ ./process rb1-gps.dat
Processing rb1-gps.dat
f =  1.081017978e-14
d = -4.280688646e-19
  tau         ADEV             drift       ADEV drift corr
    600  6.497785589e-12 -2.568413188e-16  6.497785586e-12
   1200  3.673171557e-12 -6.227037798e-17  3.673171556e-12
   3000  2.152493532e-12 -1.038649600e-15  2.152493406e-12
   6000  1.229699919e-12 -8.085623481e-16  1.229699786e-12
  12000  5.983794472e-13 -3.352669661e-16  5.983794003e-13
  30000  3.088139889e-13 -3.005567023e-15  3.088066758e-13
  60000  2.375139899e-13 -7.098259175e-15  2.374609500e-13
 120000  2.408230821e-13 -1.121038732e-14  2.406925850e-13
 300000  2.703779963e-13 -1.747740334e-14  2.700954111e-13
 600000  2.336053294e-13 -3.031742721e-14  2.326195966e-13
1200000  1.439223207e-13 -4.724838750e-14  1.399908188e-13
3000000  1.847594665e-13 -2.018394038e-13  1.173306781e-13
6000000  2.953067943e-13 -4.161066973e-13  2.517361716e-14

The frequency and drift measure are just averages over the available samples.

The ADEV(tau) measure is a schoolbook variant and seems to match your plot
well, as expected.
The drift(tau) measure is a drift measure calculated over different tau ranges
as average.
The ADEV_driftcorr(tau) measure is the schoolbook ADEV variant with the
drift(tau) estimate compensated out from the measures before squaring.

As you see, as tau increases the drift(tau) measure rises and as the curves
come closer, the drift rate polution into the data becomes more prominent.

I have included higher tau values even if their ADEV measures isn't numerically
very stable yeat. The measurement period is a bit short (21416 samples)
compared to the higher tau0 multiples (5000 and 10000). 

> Similarly CS1 (a later model 5061A also with late OCXO and replacement
> FTS tube) ran at about -2.5x10e-13 for the first 70 days of the run, and
> for quite a long time prior to that.  But starting at the 70 day point,
> it went into a series of slow oscillations with a mean offset of about
> zero; recent data shows that it may be returning to the historic offset.
>  Looking at the first 70 days with the offset removed, there's very
> little discernable linear drift; instead most of the instability appears
> to be various cycles ranging from daily to a couple of weeks.

Arbitrary removal of data for it to "look good" can be a good way of fooling
yourself, but you already know that.

> And, for anyone who's interested in playing with the data, I've uploaded
> it to http://www.febo.com/time-freq/uploads/.  There are three files in
> the zip, which is about 327k.  Each consists of MJD and phase data with
> a base tau of 600 seconds.



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