[time-nuts] GPS 1 PPS Averaging ?

Brooke Clarke brooke at pacific.net
Sun Mar 13 15:14:33 EST 2005

Hi John:

But the data does not include the variation we get because of the 
sawtooth error in the Motorola GPS receivers.   I'm using an old 8 
channel UT+ timing receiver with the asymmetrical sawtooth error.  Maybe 
if I get one of the newer M12+Timing receivers and correct the sawtooth 
either in software or hardware then I could approach the numbers shown 
on the NIST GPS archive web page.  The ideal would be an Ashtech Z12 
setup for carrier phase time transfer.

Based on Tom's post suggesting looking at one day prompted me to look at 
what averaging is needed for one day readings, hence the subject post.

I'm going to try 5,000 second averages to try and reduce the GPS 1 PPS 
variation.  The SR620 can only average in a 1, 2, 5 * En sequence up to 
5E6 readings.  It would be nice to be able to do 86400 second averages.

Have Fun,


John Ackermann N8UR wrote:

> 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
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