# [time-nuts] GPS 1 PPS Averaging ?

Brooke Clarke brooke at pacific.net
Sun Mar 13 14:26:30 EST 2005

```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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```