[time-nuts] Disciplining dual oscillators using a 3-corner hat

[Bruce Griffiths]

Richard H McCorkle wrote:
> Hello Time-Nuts,
> I am currently disciplining two MTI260 oscillators in a
> dual standard to a common GPS timing receiver 1PPS with
> two highly modified Shera style controllers that use a
> 100 MHz TIC with sawtooth correction and a 23-bit DAC.
> Phase samples are accumulated over identical 30-second
> periods between updates and the updates are logged over
> identical sample intervals from both controllers using
> a common receiver. When the phase data from the two
> controllers are compared there is a striking similarity
> in the short-term phase variations in both data sets
> when both oscillators are locked.
>   Extreme care was taken to minimize coupling between
> the oscillators by using separate power supplies,
> physical separation, and shielding of the two systems
> and their associated wiring. Intentionally varying the
> frequency in either of the oscillators has no visible
> effect in the phase data from the other oscillator so
> I don’t believe injection locking is occurring between
> the oscillators.
>   The MTI260 has very good short-term stability so I am
> assuming the short-term phase variations of nanoseconds
> per update seen in both data sets are predominantly the
> result of changes in the GPS 1PPS timing. I am wondering
> if anyone on the list has explored the concept of using
> the common phase variations from multiple disciplined
> high-stability oscillators driven from a common GPS
> receiver to determine the actual GPS variation (using a
> 3-corner hat analysis) and apply that information in the
> disciplining routines to improve oscillator short-term
> stability.
>   I am considering a methodology of doing comparisons of
> A to GPS in controller A, B to GPS in controller B, and
> then having the two controllers share their phase data
> and do a comparison in each controller to determine the
> common GPS variation and correct the raw phase data before
> calculating the EFC. Each controller outputs the combined
> phase effects of the GPS and its oscillator and by sharing
> the phase data between two controllers fed by a common
> receiver I believe the GPS variations in the raw phase
> data could be eliminated using simple PIC math as shown
> in the following equations using Gp as the GPS phase, Ap
> as the A oscillator phase, and Bp as the B oscillator phase.
>
> Controller A raw phase data = (Gp + Ap)
> Controller B raw phase data = (Gp + Bp)
> Difference in readings = (Gp + Ap) – (Gp + Bp) = (Ap – Bp)
> A reading – difference = (Gp + Ap) – (Ap – Bp) = (Gp – Bp)
> B GPS difference = (Gp + Bp) + (Gp – Bp) = (Gp * 2)
> GPS phase data = (Gp * 2) / 2 = Gp
> Controller A corrected phase data = (Gp + Ap) – Gp = Ap
> Controller B corrected phase data = (Gp + Bp) – Gp = Bp
>
>    One concern I have is a 3-corner hat is generally
> performed on three sources of similar stability. In
> this case the short-term stability of the two MTI260
> oscillators will be much better than the GPS short-term
> stability and I am questioning how valid the data will be.
> I would appreciate any comments on the concept, flaws in
> the methodology, or pitfalls that might result during
> implementation before I attempt this in a working system.
>
> Thanks for your input,
>
> Richard
>   
Richard

1) The above is not a 3 cornered hat comparison.
You have to compare oscillators A and B directly with each other as well.
The 3 cornered hat technique assumes that the phases of all 3 
oscillator  are statistically independent.
This assumption almost inevitably fails for sufficiently long Tau. (In 
your case when Tau is a significant fraction of the averaging time.)

If the oscillators/frequency sources  are statistically independent then 
one can determine the individual instabilities from measurements of the 
3 phase differences, however one cannot determine the individual phase 
errors for each oscillator.

If all one source has significantly greater instability than the other 2 
then the accuracy in determining the instability of the other 2 suffers.

2) Your maths is incorrect, The 4th line should be:

A reading – difference = (Gp + Ap) – (Ap – Bp) = (Gp + Bp)

Thus as one should expect you technique doesnt work, with only 2 measurements you cannot determine 3 quantities.

The only way you are going to significantly improve the performance of 
your GPSDOs is to use GPS carrier phase measurements, the 
Rockwell/Connexant/Navman Jupiter receivers have the GPS carrier phase 
data available. However to be useful the receiver local oscillator has 
to be phase locked to the OCXOs being disciplined.

Bruce