[time-nuts] Comments on ADEV, MDEV, TDEV, etc
Tom Clark, K3IO
K3IO at verizon.net
Wed Apr 11 01:33:38 EDT 2007
I'll try to answer several of the questions at one time
Brooke (no relation) Clarke
Why is the Datum2000 so much better than the other receivers?
It is a GPSDO. It is pretty obvious that the "handover" from the
2000's Rb to GPS is at ~1,000-10,000 seconds.
Brooks Shera:
In view of recent interest in the Allan Deviation of GPS-based 1
pps time,
it should be mentioned that the calculation of ADEV is based on a
statistical model which is not completely appropriate for noise
sources
present in GPS signals and their decoding hardware/software. For
example, white phase noise,
which results from quantization effects in GPS receivers (sawtooth)
and in
counter-based TICs.
The result is that ADEV plots can be misleading if used to compare
the
performance of clocks or signals with dissimilar noise properties.
Allan
pointed this out in his 1981 paper in 'Proc. 35th Ann. Freq.
Control
Symposium', and proposed a "modified" ADEV (MDEV) as a solution.
He wrote:
"A direct application for using the modified allan variance
recently arose
in the analysis of atomic clock data as received from a GPS
satellite.
...Using Mod AV we can tell that the fundamental limiting noise
process
involved in the system is white noise PM with the exciting result
that
averaging for four minutes can allow one to ascertain time
differences to
better that one nsec."
Here's my explanation of the difference between the ADEV & MDEV.
For the ADEV, you compare the actual indicated time on a clock with
the time you would have predicted on that clock from an earlier
measurement. Repeat that measurement a number of times and take the
Standard Deviation of the difference. Example: for the past week, I
have noticed that my wrist watch gains, on average, 10 seconds per
day. The individual differences between my watch and WWV over this
week have been 0,10,19,31,41,49,59 & 70 sec, so that the daily error
from the average is 0,-1,+1,+1,-1,-1 & 0. I compute the Std Dev of
those 7 numbers to be 0.9 seconds and, since the elapsed time between
the measurements was 86400 seconds, the ADEV value @1-day = 0.9/86400
= 1.04e-5. Notice that this was computed by just taking the one-way
differences between t and t+dt. Also notice that I chose to remove the
average 10 sec/day, since that was totally predictable. You can get a
good description of ADEV, including its application to George
Harrison's original clocks, in the appendices of HP Application Note
#1289 ("The Science of Timekeeping") available on
[1]http://gpstime.com -- all Time Nuts MUST have a copy of HP1289 --
it's a real classic!
The MDEV involves a 2-sided difference, comparing the indicated time
at t with the value linearly interpolated between t-dt and t+dt -- and
this interpolation process removes many artifacts that may occur with
an oscillator that drifts. For the numbers in my example, we get 6
numbers: +½, -1½,1, 1, -1 & -½. The Std Dev = 1.07s and the MDEV =
1.24e05 @ 1 day. Usually, the MDEV will be lower than the ADEV for
more "real" oscillators.
Instruments like the TSC5110/15/20 can only compare "now" with "old"
and cannot see into the future. Therefore these instruments only
produce ADEV.
In general, you want to use ADEV as a statistical descriptor of the
"now" instantaneous performance of a clock. If you are trying to
construct a "paper clock" that can be used to help tweak the twiddle
pot on a Rube, or if you are analyzing long streams of data, then MDEV
is better. This situation applies to the problem that David Allan was
solving that Brooks quoted above.
Bruce Griffiths noted
The plots are not conclusive evidence that correcting for the
sawtooth error isn't advisable.
What about "hanging bridges" and similar artifacts?
Several people, including Brooks, noted that sawtooth errors screw up
simple ADEV plots, especially with "hanging bridges". I would note
that all of my plots assume that the gross sawtooth (and, by
implication, hanging bridges) from Motorola receivers has been removed
as a part of the data acquisition process. The resulting "clock noise"
of GPS vs a H-Maser atomic clock (with sawtooth removed) is quite
noise-like and with an RMS level ~2-3 nsec over intervals like 5
minutes (i.e. ~300 samples). I've looked from hanging bridges and find
none.
In the CNS-2, Rick has implemented a hardware de-sawtoother and we
have now demonstrated that the software and hardware corrections are
the same at the 1 nsec quantization level. The programmable delay line
is doing its thing! (see the 2005 & 2006 papers on
[2]http://gpstime.com for more details).
Poul-Henning noted
This is simply not true. No averaging period can ever guarantee you
will not get a constant offset from the sawtooth. You may get rid
of the noise, but not the bias.
When the sawtooth is running with its typical period ~5-15 seconds,
then a simple running average does remove the bias. The
de-sawtoothing, in either hardware or software, DOES remove any
residual "hanging bridge" biases.
Also a question about TDEV came up. TDEV is simply the expected error
in clock units, and is obtained as ADEV*dt, where dt is the time
interval in question. You can also form a Modified TDEV as MDEV*dt.
I know it was mentioned earlier, but the "bible" on all these *DEV
topics is the User Manual from Bill Wriley's STABLE32 (see
[3]http://www.wriley.com/) and his various papers. Several of us (TvB,
Rick & me for 3) find that STABLE32 is one of the most useful software
packages ever written; well worth the ~$400 it costs.
Regards, Tom
References
1. http://gpstime.com/
2. http://gpstime.com/
3. http://www.wriley.com/
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