From: "Brooks Shera" ebs@wildblue.net
Subject: [time-nuts] Oops - wrong URL for tvb plot!
Date: Mon, 9 Apr 2007 20:10:12 -0600
Message-ID: 00a301c77b15$652a5030$6500a8c0@EBS8500

Phew, I was kind of worried there for a while. The ADEV plot showed three
straight parallel lines with no tendendency to converge.

Interesting to (finally) see MDEV used for this analysis.

Cheers,
Magnus

Me too. Using ADEV to look at the three receivers seemed like
the obvious thing to do, but then Brooks suggested I look at
MDEV instead and I was very surprised, and pleased, to see
the result. It much better reflects what we all do with GPS
receivers, something Tom Clark first popularized with his VP
TAC a decade ago -- which is to time average the sawtooth
away [ OK, for the purists: not to average away to zero, but
to reduce it somewhat through short-term averaging ].

The other thing about the plot is that it show a nice real world
example where using ADEV doesn't convey the right message
at all; using MDEV is closer to the truth.

/tvb

From: "Tom Van Baak" tvb@LeapSecond.com
Subject: Re: [time-nuts] Oops - wrong URL for tvb plot!
Date: Tue, 10 Apr 2007 07:46:30 -0700
Message-ID: 008b01c77b7f$06f91a40$c1ac1cac@pc52

Indeed. I have long wondered why you guys are not using MDEV or at least ADEV
and MDEV.

Did you drift-rate compensate the measures before ADEV/MDEV them?
That's another real world effect one may need to handle. For GPS receivers
against a good reference (H/CS) it may not be such a big issue thought. It
should be interesting to pull the drift rate values out and plot them alongside
to see when they take over.

Cheers,
Magnus

From: Magnus Danielson cfmd@bredband.net
Subject: Re: [time-nuts] Oops - wrong URL for tvb plot!
Date: Tue, 10 Apr 2007 17:28:40 +0200 (CEST)
Message-ID: 20070410.172840.-1382150419.cfmd@bredband.net

Infact, if you send me the raw data I could process them and see what pops up.
I have some code lying around already. Should get into the habit of doing some
cheesy plots (gnuplot maybe).

Cheers,
Magnus

I don't normally remove phase drift (frequency offset)
as this drops out of any adev calculation.

The raw data is there too: http://www.leapsecond.com/pages/3gps/

/tvb

From: "Tom Van Baak" tvb@LeapSecond.com
Subject: Re: [time-nuts] Oops - wrong URL for tvb plot!
Date: Tue, 10 Apr 2007 09:27:08 -0700
Message-ID: 000301c77b8d$16299ea0$c1ac1cac@pc52

I was talking about frequency drift rate, it is usually shorted into drift
rate. This is not canceled at all by either ADEV or MDEV. Frequency offsets
cancel naturally.

Great! Thanks!

Cheers,
Magnus

Magnus,

I can see the danger now of a plot without any accompanying text.
The raw data for the three 12 hour Motorola receivers is here:
http://www.leapsecond.com/pages/3gps/
I'm on vacation right now, but I'm pretty sure these were taken
with a 53132A against a good atomic house standard. You'll
see a large phase offset (many microseconds), a frequency
offset (about +3e-12 or -3e-13). No, I didn't remove frequency
drift (if any) from the data before I plotted it.

/tvb

From: "Tom Van Baak" tvb@LeapSecond.com
Subject: Re: [time-nuts] Oops - wrong URL for tvb plot!
Date: Tue, 10 Apr 2007 14:26:27 -0700
Message-ID: 001401c77bb6$e6bcddb0$c1ac1cac@pc52

Tom,

As always.

OK. I'll see what I can do. I beleive I already have something, but I think I
will have to massage it to do anything but ascii-tables.

The phase and frequency offsets will naturally be canceled out by ADEV and
MDEV. It is interesting to plot compensated and non-compensated data alongside
each other with the drift there too.

What do you use for generating the plots? GnuPlot?

Cheers,
Magnus

From: "Tom Van Baak" tvb@LeapSecond.com
Subject: Re: [time-nuts] Oops - wrong URL for tvb plot!
Date: Tue, 10 Apr 2007 14:26:27 -0700
Message-ID: 001401c77bb6$e6bcddb0$c1ac1cac@pc52

Tom,

OK. A very quick adaptation using the same program I used for the Febo
Cs1/Cs2/Rb data give these runs:

Processing vp-1pps.dat

Bias report
t =  1.608663494e-04
f =  2.770643453e-12
d = -6.750613692e-13

Deviation report
tau        ADEV            drift          ADEV drift    ADEV drift corr      MADEV      MADEV drift corr
1  4.496133759e-08 -6.750613692e-13  4.773404719e-13  4.496133759e-08  4.496133759e-08  4.496133759e-08
2  2.865449852e-08 +3.636859572e-14  5.143296131e-14  2.865449852e-08  2.156096803e-08  2.156096803e-08
5  1.023033819e-08 -3.068109484e-13  1.084740511e-12  1.023033814e-08  5.035764941e-09  5.035764883e-09
10  5.467657422e-09 -9.345581882e-15  6.608324323e-14  5.467657422e-09  1.851770267e-09  1.851770292e-09
20  2.739243283e-09 +1.598685109e-14  2.260882162e-13  2.739243274e-09  6.821017995e-10  6.821018772e-10
50  1.093507243e-09 +5.205704132e-15  1.840494346e-13  1.093507227e-09  1.715728448e-10  1.715728594e-10
100  5.454287557e-10 -6.415818074e-16  4.536668467e-14  5.454287538e-10  6.120960706e-11  6.120958759e-11
200  2.703346601e-10 -1.108422405e-16  1.567545998e-14  2.703346596e-10  2.191194834e-11  2.191193475e-11
500  1.093861099e-10 +2.921066096e-17  1.032752822e-14  1.093861094e-10  6.412724502e-12  6.412726902e-12
1000  5.457886650e-11 +1.802704891e-17  1.274704853e-14  5.457886502e-11  2.565426688e-12  2.565390448e-12
2000  2.708262717e-11 -2.666445822e-17  3.770923845e-14  2.708260091e-11  8.491241117e-13  8.457943641e-13
5000  1.095479778e-11 -2.350726513e-17  8.311073291e-14  1.095448251e-11  2.883950982e-13  2.965846010e-13
10000  5.449823758e-12 -2.243416118e-17  1.586334750e-13  5.447514517e-12  3.021670741e-13  1.702555808e-13
20000  2.759576507e-12 -3.330702851e-17  4.710325145e-13  2.719079048e-12 -0.000000000e+00 -0.000000000e+00

Processing cns-1pps.dat

Bias report
t =  1.600450573e-04
f =  2.913835034e-12
d =  7.500681880e-14

Deviation report
tau        ADEV            drift          ADEV drift    ADEV drift corr      MADEV      MADEV drift corr
1  1.577095429e-08 +7.500681880e-14  5.303783021e-14  1.577095429e-08  1.577095429e-08  1.577095429e-08
2  7.681160884e-09 -1.636586807e-13  2.314483259e-13  7.681160881e-09  5.415005871e-09  5.415005862e-09
5  3.078415865e-09 +2.509775393e-14  8.873395999e-14  3.078415864e-09  1.361031473e-09  1.361031473e-09
10  1.560186382e-09 -1.102824139e-14  7.798144274e-14  1.560186380e-09  4.738158072e-10  4.738158043e-10
20  7.798503527e-10 -7.791528277e-15  1.101888496e-13  7.798503449e-10  1.790275974e-10  1.790276051e-10
50  3.127308712e-10 -1.816028065e-15  6.420628798e-14  3.127308646e-10  5.422110976e-11  5.422112463e-11
100  1.584470437e-10 +8.630531074e-17  6.102707048e-15  1.584470436e-10  2.574021466e-11  2.574020071e-11
200  7.909625288e-11 +2.777076930e-16  3.927379858e-14  7.909624313e-11  1.050007533e-11  1.050024793e-11
500  3.205724824e-11 +4.136006326e-17  1.462299060e-14  3.205724491e-11  3.743227983e-12  3.743161194e-12
1000  1.592153776e-11 +8.830182390e-17  6.243881847e-14  1.592141533e-11  1.742977833e-12  1.742820380e-12
2000  8.001780034e-12 +2.310428021e-17  3.267438643e-14  8.001713322e-12  9.412214466e-13  9.412798792e-13
5000  3.255675022e-12 +2.633754927e-17  9.311729843e-14  3.254343101e-12  5.166966738e-13  5.179242182e-13
10000  1.628568806e-12 -3.689307442e-18  2.608734310e-14  1.628359852e-12  2.251512130e-13  2.037213874e-13
20000  7.937637120e-13 -4.168959480e-18  5.895799037e-14  7.915710870e-13 -0.000000000e+00 -0.000000000e+00

Processing cns2-1pps.dat

Bias report
t =  4.809698766e-06
f = -4.750323886e-13
d = -2.045640513e-14

Deviation report
tau        ADEV            drift          ADEV drift    ADEV drift corr      MADEV      MADEV drift corr
1  3.040349710e-09 -2.045640513e-14  1.446486278e-14  3.040349710e-09  3.040349710e-09  3.040349710e-09
2  1.509947204e-09 +5.682593081e-15  8.036400204e-15  1.509947204e-09  1.076505673e-09  1.076505673e-09
5  6.266960438e-10 +4.364826771e-15  1.543199304e-14  6.266960436e-10  2.869965363e-10  2.869965353e-10
10  3.148999828e-10 +9.550229660e-16  6.753032155e-15  3.148999827e-10  1.133942495e-10  1.133942491e-10
20  1.644818676e-10 +2.593384594e-15  3.667599666e-14  1.644818635e-10  6.136054942e-11  6.136054016e-11
50  7.457270904e-11 +1.477060458e-15  5.222197332e-14  7.457269075e-11  3.193493744e-11  3.193493587e-11
100  4.169473933e-11 -2.331156674e-16  1.648376692e-14  4.169473607e-11  1.940095259e-11  1.940091575e-11
200  2.200754349e-11 -1.725996605e-16  2.440927808e-14  2.200752995e-11  9.311192242e-12  9.311282574e-12
500  9.181425432e-12 -6.932415461e-17  2.450978991e-14  9.181392717e-12  3.417399863e-12  3.417697168e-12
1000  4.884844476e-12 +3.584932616e-17  2.534930163e-14  4.884778702e-12  1.648103405e-12  1.648096413e-12
2000  2.481602408e-12 +3.268600930e-17  4.622499765e-14  2.481171852e-12  8.672402194e-13  8.677237253e-13
5000  1.226006674e-12 -3.996599800e-17  1.413011410e-13  1.217836751e-12  5.364543130e-13  5.210280149e-13
10000  5.560201741e-13 +9.211600967e-19  6.513585509e-15  5.559820206e-13  1.500836169e-13  1.448395041e-13
20000  2.290070692e-13 -7.158016508e-18  1.012296403e-13  2.054185914e-13 -0.000000000e+00 -0.000000000e+00

What you will notice here is that for these measures, they are short enought
not to be greatly limited by the ADEV drift line. Also notice that I calculate
this on a per tau basis, since the effective drift as it bias the ADEV and MDEV
calculation is actually calculated as an average and then removed before
further accumulation. The MDEV will actually weight certain drift-samples
higher than others, but this have not been used, but the ADEV drift estimator
was used in its place. The correction for this is however straighforward.

Also notice that the ADEV drift-line is calculated out from the drift estimator
drift(tau) by multiplying with tau divided by the square root of 2.

I also notice that our ADEVs deviate from each other. Hmm. Ah, I must look in
your overlapping column! Then they seem to match fairly closly.

I only made 1,2,5 steps, but I could to any integer multiple of tau with
trivial top-level modification.

Cheers,
Magnus