[time-nuts] Predicting clock stability from thevariouscharacterization methods

[Dr Bruce Griffiths]

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
>
>   
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>   
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