[time-nuts] GPS: ADEV or MDEV?

Dr Bruce Griffiths bruce.griffiths at xtra.co.nz
Mon Apr 9 21:26:54 EDT 2007

Brooks Shera wrote:
> 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
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The plot you are referring to is surely:


The VP is still distinctly worse until tau > 1000sec.

The plots are not conclusive evidence that correcting for the sawtooth 
error isn't advisable.
What about "hanging bridges" and similar artifacts?


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