[time-nuts] GPS: ADEV or MDEV?

[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."

The impact of time averaging  to suppress white phase noise is illustrated
by a new plot TVB has created and placed on his website
 http://www.leapsecond.com/pages/3gps/gps-adev.gif.

These revealing plots show that just a few hundred-second time average has 
largely removed the performance
difference between the aged VP and the newer M12+ and has almost entirely
removed the benefit of sawtooth correction (CNS-CNS II).  These important
results are not evident in the usual ADEV plot.

Such a time averaging effect is not entirely unexpected.  In the long run,
the averaged time jitter in the transmission path between the satellite and
the ground must approach zero.  What IS surprising is that the noise
averages to zero rather quickly and for purposes that require time
filtering, e.g. a GPSDO, it can safely be ignored.


Regards, and have fun,  Brooks