[time-nuts] Setting loop TC using thunderbolt internal data.

Bruce Griffiths bruce.griffiths at xtra.co.nz
Mon Jan 26 17:01:17 EST 2009


Bruce

If the Allan deviation plot is symmetric about the minimum then the
Allan intercept and the minimum have the same value of tau.
If the plot is asymmetric about the minimum then the Allan intercept and
the minimum dont share the same value of tau.
The shift is usually around 24% or less with the Allan intercept tau
shifted to the steeper slope side of the minimum.

The Hadamard deviation is insensitive to linear frequency drift, however
it has a different phase noise transfer function than the Allan deviation.
Thus the Hadamard minimum is at best indicative of the Allan intercept
location when linear frequency drift is corrected.

NIST SP1065 (http://tf.nist.gov/timefreq/general/pdf/2220.pdf) is a good
starting point as it includes a comprehensive set of references.
However one should bear in mind that ADEV, OADEV, TOTDEV, Theo_1 etc are
merely estimators for the Allan deviation.
ADEV is not the Allan deviation it is merely a poor estimator for it.
The other estimators make progressively more effective use of the data.

Bruce

Bruce Walker wrote:
> The data I posted came from a 10 hour run collecting data every
> second.  I could certainly set up other longer experiments.
>
> We quickly arrive at the limits of my experience...I had never looked
> at Hadamard deviation before.  I was curious to see what I could learn
> about the Tbolt without having anything better to measure it against.
> For the time being, this is my "lab" reference.
>
> Let me see whether I understand what I've measured.  The Allan
> intercept for my tbolt's undisciplined oscillator as measured by the
> onboard GPS solution is on order tau=800s.  The Hadamard intercept
> under the same conditions appears to be more like 1600s.   Does that
> tell me that if the disciplining model includes a drift compensation,
> the optimal disciplining time constant is close to the Hadamard
> intercept tau, but if there were no drift model, the Allan intercept
> would be more appropriate?
>
> And a primer or reference to the other statistical measures you
> mentioned (Theo_1, etc.) would be appreciated.
>
> --bruce W1BW
>
> On Mon, Jan 26, 2009 at 3:36 PM, Bruce Griffiths
> <bruce.griffiths at xtra.co.nz> wrote:
>   
>> Bruce
>>
>> What was the record length?
>>
>> TOTDEV and TOTHadamard should give more reliable estimates over a
>> greater tau range.
>>
>> Bias corrected Theo_1 and the Hadamard equivalent should be even better
>> at longer tau.
>>
>> Bruce
>>
>> Bruce Walker wrote:
>>     
>>> Thanks for the suggestion.  Here is a composite plot with Allan and Hadamard
>>> deviations for my tbolt run last night with disciplining disabled.  I think
>>> I computed Hadamard correctly.
>>>
>>> OADEV (blue) has a minimum of 9.6e-12 around tau=790
>>> OHDEV (red) has a minimum of 4.9e-12 around tau=1660
>>>
>>> --bruce W1BW
>>>
>>>
>>> On Mon, Jan 26, 2009 at 2:05 PM, Bruce Griffiths <bruce.griffiths at xtra.co.nz
>>>
>>>       
>>>> wrote:
>>>>
>>>>         
>>>       
>>>> Some idea of the shift in the minimum can be gleaned by plotting the
>>>> Hadamard deviation vs tau.
>>>>
>>>> Bruce Walker wrote:
>>>>
>>>>         
>>>>> I ran the same test as Bruce Griffiths on my tbolt; that is, I turned off
>>>>> osc disciplining altogether and created an OADEV plot from the internal
>>>>> phase measurements taken from its GPS solution.  The plot is attached.
>>>>>
>>>>>           
>>>>  It
>>>>
>>>>         
>>>>> has a minimum of about 1e-11 at tau=800, and it has the sane general
>>>>>
>>>>>           
>>>> shape
>>>>
>>>>         
>>>>> as Griffiths'.
>>>>>
>>>>> The next experiment I plan to do is to repeat the same thing using manual
>>>>> holdover mode rather than "Disable disciplining".  That should continue
>>>>>
>>>>>           
>>>> to
>>>>
>>>>         
>>>>> try to compensate for temperature and long-term drift (just not steered
>>>>>
>>>>>           
>>>> by
>>>>
>>>>         
>>>>> GPS), whereas the data taken last night use a fixed DAC.
>>>>>
>>>>> --bruce W1BW
>>>>>
>>>>>
>>>>>
>>>>>           
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>
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