# [time-nuts] GPS 1 PPS Averaging ?

John Ackermann N8UR jra at febo.com
Sun Mar 13 14:57:31 EST 2005

```Hi Brooke --

As you well know, I'm still learning my way around this stuff.  I've
done plots of a standard vs. raw GPS using anything from 100 second to
3600 second (1 hour) averages.  Recently, Tom suggested reducing data to
1 day when looking at the Cesium offset.

Recently someone gave a link to the NIST GPS data archives --
http://tf.nist.gov/timefreq/service/gpstrace.htm -- which they've (I
think) recently redone to make the data format much more useful.  What's
really interesting is that they show plots of the GPS constellation vs.
UTC(NIST) using 1 hour averages.  Yesterday, the range was about 8ns,
while over ten days the range was 22ns, and there  was almost no
increase out to 30 days.  There's a definite daily pattern in the data.

Their AVAR data shows about 5x10e-13 at one hour, and around 4x10e-14 at
24 hours.

From that, I gather that a 1 hour average may be usable, but as Tom
said, if you're patient enough, using 1 day averages is probably the
right way to get useful offset data and avoid chasing after ghosts.

John
----

Brooke Clarke wrote:

> Hi:
>
> Is this line of reasoning correct?
>
> When I average the raw GPS 1 PPS using 100 to 1,000 pulses and look at
> the standard deviation (assuming everything else is OK) it's in the
> mid 30 ns area.
>
> So when the time interval between a single raw GPS 1 PPS and a perfect
> clock is measured the expected error would be +/- 3 * Sigma or about
> 100 ns.
>
> Comparing two of these readings that are 24 hours apart would have an
> observation error of 200 ns/86,400 sec or about 2.3E-12.  The 200 ns
> comes from the starting observation being say +100 ns and the ending
> observation being - 100 ns.
>
> To get better would take either waiting many more days or averaging
> the time interval to reduce the uncertainty.  Averaging gets the
> result much faster.  Now the question is how much averaging to use?
>
> Averaging improves the measurement proportionally to the square root
> of the number of averages.  With 100 second averages 2.3E-13 could be
> seen in 24 hours, and with 10,000 second averaging 2.3E-14 could be
> seen in one day.
>
> To compute the Allan deviation using a series of measurements the
> amount of averaging on the GPS 1 PPS would need to be such that the
> GPS noise was much smaller than the uncertanity of what's being measured.
>
> Have Fun,
>
> Brooke Clarke, N6GCE

```