[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.


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

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