# [time-nuts] Training period for a Rb clock using GPS

Abhay Parekh parekh at berkeley.edu
Thu Jun 3 16:02:01 UTC 2010

```Hi Hal,
Thanks so much for the detailed post. I have a follow up question: What is
the relationship between
the training time and the appropriate value of the time constant (currently
set at 18 hours)? The time constant isn't the size of
a moving average window is it?
Thanks again for your help. We are a bit clueless here but trying to
learn...
=Abhay

On Wed, Jun 2, 2010 at 2:02 AM, Hal Murray <hmurray at megapathdsl.net> wrote:

>
> parekh at berkeley.edu said:
> > I am a newbie at this, but have been playing around with 2 prs10s. For
> our
> > application we need to run the clocks without gps, but we do get to sync
> it
> > to gps *initially* for as long as we want. However, what we've noticed is
> > that when we train it for short periods of time (< 1 hour a day) the
> clock
> > drifts for a few microseconds a day once we've disconnected gps, but when
> we
> > train it for say 12 hours, its drift seems to be much less (sub sub
> > microsecond/day). We were wondering why this should be so!
>
> Look at it the other way.  How long should it take to train it?
>
> Let's use rough numbers.
>  There are 1E5 seconds per day.
>  Your "few" microseconds is 1E-6 seconds.
>    That's an accuracy of 1 part in 1E11.
>  Your "sub-sub" is 1/10 microsecond or 1E-7 seconds.
>    So that's an accuracy of 1 part in 1E12.
>
> The data sheet says:
>  Aging (after 30 days)  <5E-11 (monthly)
> 5E-11 is 50E-12, so that's 2E-12 per day which is what you saw.
>
> The data sheet also says:
>  The PRS10 can time-tag an external 1 pps input
>  with 1 ns resolution. These values may be reported
>  back via RS-232, or used to phase-lock the unit to an
>  external reference (such as GPS) with time constants
>  of several hours.
>
> There are 4E3 seconds in an hour and 1E9 nanoseconds per second.  So in an
> hour, you can get close to 1 part in 1E12.  But that's assuming that the
> input PPS signal is right-on.
>
> There are two types of GPS receivers.  Most use a free running clock and
> generate the PPS pulse with the closest clock edge.  They typically have
> noise on the order of 15-50 ns.  Fancy ones will tell you how far off they
> think it is.  The really fancy ones will have a VCXO so they can slew the
> clock to the right offset.
>
> One magic word is "hanging bridges".  It comes up in discussions
> occasionally.
>
> For lots of info on that area:
>  http://www.gpstime.com/files/PTTI/PTTI_2006.pdf
> 31 pages, lots of good stuff, aka time sink.
>
> More here:
>  http://www.leapsecond.com/pages/vp/heater.htm
> 2 or 3 screens, good stuff, a quick read.
>
> So with only an hour, it's not unreasonable that you are off by a factor of
> 10, but you might have to get unlucky for a hanging bridge to get you.
>
> But there is another factor to consider.  What sort of filter is the
> software
> using between the PPS input and the knob that adjusts the frequency?
>
> More from the data sheet:
>  When tracking an external input, the time constant can
>  be set from 5 minutes to 18 hours.
>
> I think the manual says the default is 65K seconds.  That's 18 hours.
>  Unless
> you changed it, that explains why 1 hour wasn't enough.  It might get
> better
> if you give it more time and/or tweak the time constant if you can only get
> 12 hours.
>
>
> --
> These are my opinions, not necessarily my employer's.  I hate spam.
>
>
>
>
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```