[time-nuts] Re: Can the ADEV of a GPSDO output ever be lower than the minimum of the ADEV of the internal oscilator and the ADEV of the GPS PPS?

Mon May 2 13:54:54 UTC 2022

Here are some extra plots and what I think is happening in the simulation.

Both TCXO and PPS data is real measured data. The PI controller adjusts 
the TCXO frequency.
Note: there is a drift in the PPS as this was measured against a a 
slightly out of tune Rb.
These are all made without any filtering, just a plain PI controller.

With Kp = 0.01 (see Kp=0.01.png attachment) the TCXO frequency with 
control (top left plot, red)Â  has similar short term (+/-5e-10) 
variation as the TXCO without control (top left plot, blue).
The phase of the TCXO with control (top right plot, yellow) tracks the 
PPS(top right plot, red and the low frequency variations are a bit 
larger than the PPS (sometimes goes outside the PPS band).
The loglog plot of the ADEV versus tau (bottom right) shows how the 
output phase (GPSDO, yellow) tracks the TCXO (blue) for small TAU and 
shorts to track the PPS ADEV (red) above tau=100 at a somewhat larger ADEV.

With Kp = 0.1 (see Kp=0.1.png attachment) the TCXO frequency with 
control (top left plot, red)Â  has a larger (+/-1-e9) short term 
variation as the TXCO without control (top left plot, blue) . This is 
consistent with the increase of the ADEV with TAU = 1.
The phase of the TCXO with control (top right plot, yellow) tracks the 
PPS(top right plot, red) much better and stays well within the PPS band. 
As far as I understand this decreased "noise" in the output phase versus 
the PPS
should lead to a down shift of the loglog slope of ADEV versus tau of 
the output phase (bottom right, GPSDO, yellow)
This downshift is exactly the same as what happens to the ADEV of the 
PPS when you decrease the short term variations of the PPS by doing 
something like PPS quantization error correction (hope I'm using the 
right word) or, when done in simulation, when you reduce the white noise 
level of of the PPS phase

Nobody will ever use this setting of Kp in practice as the short term 
variations are double compared to the level with Kp=0.01

So if the phase of the output frequency has less noise than the PPS and 
you are able to keep the output phase perfectly in the middle of the PPS 
noise band the ADEV of the phase of a GPSDO output signal may (according 
to this simulation) become lower than the PPS.

What happens when you add a Kalman filter between the PPS and the 
controller? This can be seen in the Kp=0.1_Kalman.png plot
The Kalman filter effectively reduces the PPS short term variations as 
the uncontrolled frequency in the top left plotÂ  is now (a bit) visible 
again). There is no impact on the longer term stability as the output 
phase band is still similar versus the PPS and thus the ADEV for higher 
tau is similar

There may be an optimum where you increase the Kp to shift the ADEV for 
higher tau just under the PPS ADEV while not yet making the small tau 
ADEV worse.

Well, now you guys probably can tell me where I am making a mistake.
Erik.

On 2-5-2022 14:06, Markus Kleinhenz via time-nuts wrote:
> Hi Bob,
>
> thanks for the heads-up. The only other source I had was a paper
> claiming similar things, but they had only done so in simulations.
> So I thought the manual of the FS740 would be the more trustworthy of
> the two.
>
> Greetings
> Markus
>
> Am 02.05.2022 um 13:38 schrieb Bob kb8tq:
>> Hi
>>
>> If you have a FS740 and measure itâ€™s performance â€¦. you likely will
>> take anything the manual says a lot less seriously â€¦.. Their ADEV
>> performance in the real world is a bit underwhelming.
>>
>> Bob
>>
>>> On May 2, 2022, at 1:42 AM, Markus Kleinhenz via time-nuts <time-nuts at lists.febo.com> wrote:
>>>
>>> Hi Erik,
>>>
>>> I just found a hint that what you are seeing may be correct after all:
>>>
>>> The Manual of the Stanford Research Systems FS740 says:
>>>
>>>     /*Predictive Filtering*//
>>>     //The superior short term stabilities of the OCXO and Rb timebases
>>>     enable the usage of//
>>>     //predictive filtering to improve the stability of the FS740 by up
>>>     to 3 times over traditional//
>>>     //methods. Predictive filtering uses state space methods to predict
>>>     the phase of the local//
>>>     //timebase relative to GNSS. The technique is quite similar to
>>>     Kalman filtering. The//
>>>     //benefit is that the FS740 can average the GNSS signal much more
>>>     effectively, resulting//
>>>     //in a significantly more stable signal with a much shorter time
>>>     constant than would be//
>>>     //possible with traditional filtering./
>>>
>>> And has the ADEV Plots I attached. The GPS curve they printed is in the
>>> realm of a sawtooth corrected M8T (<1e-12 @ tau=10ks) [See the Plot from
>>> John Ackermanns Ublox evaluation]. But especially the Rb option seems to
>>> surpass the reference in a parallel fashion.
>>>
>>> My two cents on simulated 1PPS Signals:
>>>
>>> One has to be careful when only using ADEV as the only characteristic
>>> for modeling the 1PPS Signal as it combines White PM and Flicker PM in
>>> one slope. So you may create an artificial signal which is pure WPN and
>>> in turn is best predicted by something like the kalman filter.
>>>
>>> Regards,
>>>
>>> Markus
>>>
>>> Am 29.04.2022 um 19:24 schrieb Erik Kaashoek:
>>>> Thanks for confirming something is still wrong. :-(
>>>> I've extended the simulation to contain a full Kalman filter working
>>>> with 2 state parameters: phase and frequency.
>>>> The biggest impact I can see is when increasing Kp above the optimal
>>>> value the PPS noise normally starts to impact the output phase and the
>>>> ADEV at tau 1 becomes worse
>>>> The Kalman filter seems to be able to filter the noise from the PPS
>>>> better so with equally high Kp the ADEV at tau =1 is about a factor 4
>>>> better
>>>> Unfortunately the high Kp of 0.1 is far from optimal and setting Kp to
>>>> 0.01 gives overall a better performance and the Kalman filter no
>>>> longer seem to have a visible impact.
>>>> Octave code for the simulation and the used data files are attached.
>>>> Also 3 plots are attached showing optimal Kp, high Kp with no filter
>>>> and high Kp with Kalman filer
>>>> I'm still seeing some weird stuff in the ADEV plots.
>>>> Erik.
>>>>
>>>> On 29-4-2022 16:53, AndrÃ© Balsa wrote:
>>>>> Hi Erik,
>>>>> Mathematically, no, a GPSDO cannot have a lower uncertainty (ADEV)
>>>>> than the
>>>>> minimum observable uncertainty (ADEV) of the combined oscillator
>>>>> (disciplined clock) and PPS (disciplining clock) from the GPS receiver.
>>>>> Unless there is some magic trick to remove the uncertainty in a clock
>>>>> that
>>>>> I am not aware of. ;)
>>>>>
>>>>> On Thu, Apr 28, 2022 at 10:03 PM Erik Kaashoek <erik at kaashoek.com>
>>>>> wrote:
>>>>>
>>>>>> I'm doing some simulations to understand the impact of a filter
>>>>>> between the
>>>>>> TIC measurement and the PI controller steering the Vtune of the OCXO.
>>>>>> With a well tuned PI controller without filter the best ADEV I can
>>>>>> get is
>>>>>> just above the minimum ADEV of an actual measured  OCXO and an actual
>>>>>> measured GPS PPS.
>>>>>> When I add an alpha-beta filter, similar to a first order Kalman filter
>>>>>> with a manually tuned Kalman gain, and using similar Kp, Ki, the
>>>>>> overall
>>>>>> performance does not change (much)
>>>>>> However with the filter its is possible to increase the Kp, Ki with a
>>>>>> factor 10 and when I use in the simulation instead of a measured PPS an
>>>>>> artificial PPS created from noise with the same ADEV as the GPS PP
>>>>>> but with
>>>>>> a very constant phase (different from the varying phase of a GPS
>>>>>> PPS)  the
>>>>>> ADEV of the GPSDO output in my simulation seems to drops below the
>>>>>> ADEV of
>>>>>> the PPS. Am I correct to assume this is a hint there is still something
>>>>>> wrong in the simulation or was my initial assumption about the possible
>>>>>> range of the GPSDO ADEV wrong?
>>>>>> Erik.
>>>>>>
>>> <FS740_ADEV.PNG><UBLOX_QERR_ADEV.PNG>_______________________________________________
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