Brooke Clarke wrote: > Hi Tom: > > Is there a way to use the Allan plot to predict the variation in a reading? > For example if you use the plot comparing the 1 PPS from a GPS receiver > to a good Cesium frequency standard, then: > (1) what size of variation would you expect if the Cesium standard was > divided down to 1 kHz and that was compared to the GPS 1 PPS, or > (2) what size of variation would you expect if the Cesium standard was > divided down to 1 Pulse/1,000 seconds? > > Have Fun, > > Brooke Clarke > > > _____________________________________________ > time-nuts mailing list > [email protected] > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > > Brooke
To answer this you will need to know the Allan deviation as a function of tau for both the caesium frequency standard and the GPS receiver output. The Allan variance of the measurement will be equal to the sum of the Allan variances of the GPS receiver and the Caesium standard for the each tau. The resultant Allan deviation will be equal to the square root of the Allan variance. This assumes that the 2 sources are uncorrelated. Eventually for a long enough tau some correlation will be found as variations in room temperature produces correlated phase shifts/delays in the caesium standard (and any associated dividers) and the GPS receiver. For most GPS timing receivers the Allan deviation of the receiver output will dominate until tau is around 1 day or so for a high quality GPS timing receiver. The value of tau at which the Allan deviations of both the caesium standard and the GPS timing receiver are comparable will be much longer for most older generation GPS timing receivers. For example a Caesium frequency standard with a standard tube will have a worst case timing errors as listed below: Tau timing error 1 120ps 10 85ps 100 270ps 1000 850ps 1 day 17ns Whereas a high quality GPS timing receiver will have an rms timing error under favourable conditions of a little better than 10ns for tau < 1 day. A carrier phase tracking GPS receiver will do much better than a typical high quality GPS timing receiver for small values of tau (< 1000 sec or so), however it will eventually be limited by the stability of the transmitted GPS carrier. A high quality quartz oscillator disciplined by a GPS carrier phase tracking receiver will outperform a Caesium frequency standard with a standard tube, for tau < 1 day, eventually it is limited by the GPS Allan deviation floor of around 5E-14 at tau = 1 day. Bruce _______________________________________________ time-nuts mailing list [email protected] https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
