Some long-term data
Hi --
I'm running an experiment with my 3 atomic standards (2 HP 5061A and 1
HP 5065A) versus GPS via an M12+ (no sawtooth correction). I now have
148 days of data, and hope to keep the experiment running out to 180 days.
For the fun of it this morning I ran all-tau analyses of all three
standards and combined them on a single chart. I also plotted the raw
phase (normalizing for scale.
I suspect there some interesting conclusions that can be drawn both
about GPS measurements in general (apropos to the recent discussion),
and the behavior of these three standards in particular, from this data;
I've come up with a few, but I bet the gang here will find more.
Attached are the ADEV and phase plots; I'm working up a web page but
don't have that ready yet.
Happy Holidays!
John
In message 458D7536.4060604@febo.com, John Ackermann N8UR writes:
I'm running an experiment with my 3 atomic standards (2 HP 5061A and 1
HP 5065A) versus GPS via an M12+ (no sawtooth correction). I now have
148 days of data, and hope to keep the experiment running out to 180 days.
180 days is a bad choice because most environmental effects have a strong
yearly component.
--
Poul-Henning Kamp | UNIX since Zilog Zeus 3.20
phk@FreeBSD.ORG | TCP/IP since RFC 956
FreeBSD committer | BSD since 4.3-tahoe
Never attribute to malice what can adequately be explained by incompetence.
Poul-Henning Kamp said the following on 12/23/2006 05:11 PM:
In message 458D7536.4060604@febo.com, John Ackermann N8UR writes:
I'm running an experiment with my 3 atomic standards (2 HP 5061A and 1
HP 5065A) versus GPS via an M12+ (no sawtooth correction). I now have
148 days of data, and hope to keep the experiment running out to 180 days.
180 days is a bad choice because most environmental effects have a strong
yearly component.
Good point... the problem is that at some point soon I need to do some
reconfiguration. The cut-off will depend on when I'm ready to rewire
the lab PPS signals, so it may be a while longer than that :-)
John
From: "Poul-Henning Kamp" phk@phk.freebsd.dk
Subject: Re: [time-nuts] Some long-term data
Date: Sat, 23 Dec 2006 22:11:20 +0000
Message-ID: 25407.1166911880@critter.freebsd.dk
In message 458D7536.4060604@febo.com, John Ackermann N8UR writes:
I'm running an experiment with my 3 atomic standards (2 HP 5061A and 1
HP 5065A) versus GPS via an M12+ (no sawtooth correction). I now have
148 days of data, and hope to keep the experiment running out to 180 days.
180 days is a bad choice because most environmental effects have a strong
yearly component.
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?
(Actually, if you hand me the raw data I would love to do some exercises on
them.)
Cheers,
Magnus
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.
(Actually, if you hand me the raw data I would love to do some exercises on
them.)
I'll be happy to ship the data to anyone who's interested. Each file is
about 600kb before compression, and it compresses well.
John
From: John Ackermann N8UR jra@febo.com
Subject: Re: [time-nuts] Some long-term data
Date: Sat, 23 Dec 2006 17:53:50 -0500
Message-ID: 458DB37E.1040504@febo.com
Hi John!
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.
(Actually, if you hand me the raw data I would love to do some exercises on
them.)
I'll be happy to ship the data to anyone who's interested. Each file is
about 600kb before compression, and it compresses well.
No problem!
Cheers,
Magnus
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.
In the data I've been working with, there is a component of linear drift
in the CS2 results; if you chop off the first 1250 records where the
offset was essentially 0 and look at the rest of the data, the offset is
about +7x10e-13 and a quadratic fit shows a drift of 6.4x10e-15/day.
What's interesting about CS2 (a fairly old 5061A upgraded with the later
model 10811A OCXO and a replacement FTS tube) is that it ran for over a
year prior to this experiment with very, very low offset; there were
certainly wobbles but the long-term offset was in the low 14s. That
shows at the beginning of the current plot, but about 20 days into the
run something changed (and I don't know what) that caused the offset to
increase.
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.
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.
John
John
From: John Ackermann N8UR jra@febo.com
Subject: Re: [time-nuts] Some long-term data
Date: Sun, 24 Dec 2006 10:51:59 -0500
Message-ID: 458EA21F.6030702@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@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@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@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.
Thanks.
Cheers,
Magnus
From: Magnus Danielson cfmd@bredband.net
Subject: Re: [time-nuts] Some long-term data
Date: Mon, 25 Dec 2006 03:43:16 +0100 (CET)
Message-ID: 20061225.034316.-1476063739.cfmd@bredband.net
Now, I made a quick little program that process the data, here is the result:
Ehum... no... forget those plots. I just realized a little error in my
drift(tau) estimator. I had a divide by tau too little, which will make the tau
rise. As I said, the devil is in the details.
Corrected it becomes the less interesting plots:
magnus@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 -2.464638917e-19 6.669673909e-12
1200 3.834415574e-12 -8.108122133e-20 3.834415574e-12
3000 2.262840286e-12 -2.392890882e-19 2.262840286e-12
6000 1.321830189e-12 -3.349535739e-20 1.321830189e-12
12000 6.871654621e-13 +3.846473719e-20 6.871654621e-13
30000 3.721752717e-13 +2.056358286e-20 3.721752717e-13
60000 2.376494277e-13 -1.810085678e-20 2.376494276e-13
120000 1.702980952e-13 +2.320652509e-21 1.702980952e-13
300000 1.549264955e-13 +3.629179727e-21 1.549264954e-13
600000 1.401676798e-13 -5.790456326e-21 1.401676797e-13
1200000 6.799762269e-14 +1.948183423e-20 6.799761934e-14
3000000 1.010049262e-13 +4.150533462e-20 1.010049006e-13
6000000 1.550028203e-13 +3.651598399e-20 1.550027944e-13
magnus@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 +1.816049729e-19 7.508211487e-12
1200 4.527916555e-12 +9.729746560e-20 4.527916555e-12
3000 2.722308557e-12 +4.515867825e-20 2.722308557e-12
6000 1.721060210e-12 -7.880496874e-20 1.721060210e-12
12000 1.035443547e-12 +9.560956213e-20 1.035443547e-12
30000 6.178807446e-13 +1.132639019e-19 6.178807443e-13
60000 4.117968150e-13 +1.218708103e-19 4.117968139e-13
120000 2.667708446e-13 +8.332110720e-20 2.667708431e-13
300000 1.831015144e-13 +7.249210859e-20 1.831015101e-13
600000 1.607481137e-13 +6.187329751e-20 1.607481066e-13
1200000 9.695302954e-14 +6.246924523e-20 9.695300539e-14
3000000 1.780291901e-13 +7.356014755e-20 1.780291445e-13
6000000 3.223233857e-13 +7.588775895e-20 3.223233321e-13
magnus@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 -4.280688646e-19 6.497785589e-12
1200 3.673171557e-12 -5.189198165e-20 3.673171557e-12
3000 2.152493532e-12 -3.462165333e-19 2.152493532e-12
6000 1.229699919e-12 -1.347603914e-19 1.229699919e-12
12000 5.983794472e-13 -2.793891384e-20 5.983794472e-13
30000 3.088139889e-13 -1.001855674e-19 3.088139884e-13
60000 2.375139899e-13 -1.183043196e-19 2.375139881e-13
120000 2.408230821e-13 -9.341989437e-20 2.408230800e-13
300000 2.703779963e-13 -5.825801115e-20 2.703779944e-13
600000 2.336053294e-13 -5.052904535e-20 2.336053261e-13
1200000 1.439223207e-13 -3.937365625e-20 1.439223143e-13
3000000 1.847594665e-13 -6.727980125e-20 1.847594298e-13
6000000 2.953067943e-13 -6.935111621e-20 2.953067454e-13
You do that drift corrections do change the numbers a bit. The distance is
however so large that for these numbers we can safely ignore drift correction.
There is a subtle point in the drift(tau) calculation, it is designed to
model the ADEV(tau) sensitivity to drift, rather than just using the overall
drift averaging. The overall drift averaging may however be a good indicator
on weither drift compensation is needed or not. With an alternative form of
ADEV can all three measures be calculated concurrently and with a much
smaller memory usage than keeping all samples and post-process it.
Cheers,
Magnus
From: Magnus Danielson cfmd@bredband.net
Subject: Re: [time-nuts] Some long-term data
Date: Mon, 25 Dec 2006 04:04:09 +0100 (CET)
Message-ID: 20061225.040409.-1066394447.cfmd@bredband.net
From: Magnus Danielson cfmd@bredband.net
Subject: Re: [time-nuts] Some long-term data
Date: Mon, 25 Dec 2006 03:43:16 +0100 (CET)
Message-ID: 20061225.034316.-1476063739.cfmd@bredband.net
Now, I made a quick little program that process the data, here is the result:
Ehum... no... forget those plots. I just realized a little error in my
drift(tau) estimator. I had a divide by tau too little, which will make the tau
rise. As I said, the devil is in the details.
Brown paperbag on the head? Yes please!
I realized this morning that I had probably made yeat another error, which I
now have done the homework on and found that yes, I did. Infact, I had two
errors which canceled each other for the ADEV corrected form but not for the
drift estimate which was correct. Mumble.
When ADEV(tau) is
---------------------------------------
/ N-2n |
/ ---
/ 1 \ 2
ADEV(n*tau0) = \ / --------------- > (x - 2 x + x )
\ / 2n²tau²(N - 2n) / i+2n i+n n
\ / 0 ---
/ i=1
The drift(tau) is
N-2n
---
1 \
drift(n*tau0) = -------------- > (x - 2 x + x )
n²tau²(N - 2n) / i+2n i+n n
0 ---
i=1
This can be concluded by letting x(t) be set to the linear assignment
delta v D 2
x(t) = TE + ------- t + - t
0 vn 2
in the inner second difference
sd(i,n) = x - 2 x + x
i+2n i+n n
and the result becomes
2 2
Dn tau
0
with that in hand it is simple enought to validate the rest of the drift(tau)
formula as given. Doing the same to the ADEV calculation gives
-
/1
ADEV (tau) = D n*tau \ / -
drift 0 / 2
Thus, for longer taus, even a small drift rate can bite us since it is now
multiplied with tau.
To compensate this I chose to subtract the Dn²tau0² part from the second
difference prior to squaring. This is equalent to preprocess the x samples
by removing the drift, however I always use drift(tau) which is the effective
average drift as it will contaminate the measure at a certain tau.
My corrected ADEV becomes:
----------------------------------------------------------
/ N-2n |
/ ---
/ 1 \ 2
ADEV(n*tau0) = \ / --------------- > (x - 2 x + x - drift(tau)n²tau²)
\ / 2n²tau²(N - 2n) / i+2n i+n n
\ / 0 ---
/ i=1
The resulting measures becomes:
magnus@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 -2.464638917e-19 6.669673908e-12
1200 3.834415574e-12 -8.108122133e-20 3.834415573e-12
3000 2.262840286e-12 -2.392890882e-19 2.262840229e-12
6000 1.321830189e-12 -3.349535739e-20 1.321830182e-12
12000 6.871654621e-13 +3.846473719e-20 6.871653846e-13
30000 3.721752717e-13 +2.056358286e-20 3.721750161e-13
60000 2.376494277e-13 -1.810085678e-20 2.376481869e-13
120000 1.702980952e-13 +2.320652509e-21 1.702979813e-13
300000 1.549264955e-13 +3.629179727e-21 1.549245826e-13
600000 1.401676798e-13 -5.790456326e-21 1.401461493e-13
1200000 6.799762269e-14 +1.948183423e-20 6.595761175e-14
3000000 1.010049262e-13 +4.150533462e-20 4.949623724e-14
6000000 1.550028203e-13 +3.651598399e-20 4.936266040e-15
magnus@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 +1.816049729e-19 7.508211486e-12
1200 4.527916555e-12 +9.729746560e-20 4.527916554e-12
3000 2.722308557e-12 +4.515867825e-20 2.722308555e-12
6000 1.721060210e-12 -7.880496874e-20 1.721060178e-12
12000 1.035443547e-12 +9.560956213e-20 1.035443229e-12
30000 6.178807446e-13 +1.132639019e-19 6.178760731e-13
60000 4.117968150e-13 +1.218708103e-19 4.117643529e-13
120000 2.667708446e-13 +8.332110720e-20 2.666771423e-13
300000 1.831015144e-13 +7.249210859e-20 1.824546103e-13
600000 1.607481137e-13 +6.187329751e-20 1.585902304e-13
1200000 9.695302954e-14 +6.246924523e-20 8.117978311e-14
3000000 1.780291901e-13 +7.356014755e-20 8.569984631e-14
6000000 3.223233857e-13 +7.588775895e-20 1.520624005e-14
magnus@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 -4.280688646e-19 6.497785586e-12
1200 3.673171557e-12 -5.189198165e-20 3.673171556e-12
3000 2.152493532e-12 -3.462165333e-19 2.152493406e-12
6000 1.229699919e-12 -1.347603914e-19 1.229699786e-12
12000 5.983794472e-13 -2.793891384e-20 5.983794003e-13
30000 3.088139889e-13 -1.001855674e-19 3.088066758e-13
60000 2.375139899e-13 -1.183043196e-19 2.374609500e-13
120000 2.408230821e-13 -9.341989437e-20 2.406925850e-13
300000 2.703779963e-13 -5.825801115e-20 2.700954111e-13
600000 2.336053294e-13 -5.052904535e-20 2.326195966e-13
1200000 1.439223207e-13 -3.937365625e-20 1.399908188e-13
3000000 1.847594665e-13 -6.727980125e-20 1.173306781e-13
6000000 2.953067943e-13 -6.935111621e-20 2.517361716e-14
magnus@heaven:~/febo$
Sigh. Well, there you have it. For longer taus, even small drift rates will
make a difference. As long as D*tau << ADEV(tau) you don't need to worry.
By the way, the modified Allan deviation is equally sensitive to drift rate.
Cheers,
Magnus