[time-nuts] GPS 1PPS ultimate accuracy

Attila Kinali attila at kinali.ch
Mon Jan 12 09:10:39 EST 2015

Ciao Andrea,

On Mon, 12 Jan 2015 11:59:26 +0100
Andrea Baldoni <erm1eaae7 at ermione.com> wrote:
> The sampling interval could come from a (long time based on a) sawtooth
> uncorrected PPS from a cheap GPS, a sawtooth corrected from a good one (perhaps
> the Lucent GPSDO), or a computer using NTP.

The GNSS Timing AppNote for the LEA6-T receiver[1] will give you an idea
what jitter you get with GPS. Please be aware that these measurements
were done with an antenna located at a _good_ position (ontop of a 4 story
building with no other high buildings around). Unless you have a simlarly
good location you will have worse performance.

Said Jackson reported some time ago that he got around 1us of jitter for
a GPS receiver (i presume it was either a LEA5-T or a LEA6-T) behind a
window. After he averaged the position for a long time (several days)
manually and stored that in the receiver he got much better performance
(sorry i cannot find the mail at the moment, you have to look for it in
the archives yourself).

NTP will give you a jitter in the range of 1-100ms, depending on
your internet connection and its conguestion. On a local network
based NTP system, you can expect jitter in the range of 10-100us IIRC.

> Each of these sources should reach a goal stability (say, 1 part in 10^13)
> after averaging them on a different (and very high I suppose) number of
> seconds (averaging them for an infinity number of seconds should give the
> stability of the underlying reference clock, but I'm willing to stop sooner...).
> I know there's no reason to go 1E-13 when the Milliren couldn't go that far,
> but the DUT may be also something else like a FE-5680A).

To get to 1e-13 with GPS (assuming 1-10ns jitter) you need somewhere around
10k to 100k seconds. At these time scales, the temperature dependent deviation
of your OCXO is likely to dominate your measurement. I would rather do
a two step measurement. If you have a FE-5680A measure its drift with a 
tau in the 100ks-200ks region. Then use the FE-5680A as refrence to measure
the drift of the OCXO in 10s-1000s timescales. If you do both continuously,
you can apply some math and get out pretty good numbers (see three cornered
hat method)

Additional to GPS jitter you also have the deviation of GPS time in
respect to TAI/UTC. This has been in recent years below 5ns (GPS vs UTC(USNO)).
But because GPS time is steered to be close to UTC it will oscillate slightly
around it. How much, i do not know. (But then the deviation between the
different UTC realizations is larger) [2]

> The sawtooth uncorrected GPS receiver may never yeld a good stability in the
> short term, but in the long one it should as well because the internal clock
> jitter would average results.

It would average out if and only if the sawtooth correction would be completely
independent of anything else. But it isn't. This results in effects where the
cycle to cycle jitter is quite low, but there is a large offset in the sawtooth
correction. This is know as "hanging bridges" in the GNSS world.

> By the way, the stability of the TAI is known or, because it's
> the reference one, it has zero deviation for definition (so you can reach
> its ultimate stability through GPS really only at the infinity...)?

There is an uncertainty number attached to TAI, but i dont know any numbers
from the top of my head. I'm sure it is mentioned in the BIPM report somewhere.

				Attila Kinali

[1] http://www.u-blox.com/images/downloads/Product_Docs/Timing_AppNote_%28GPS.G6-X-11007%29.pdf

[2] "GPS time and its steering to UTC(USNO)", presentatin by Edward Powers, 2009

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