[time-nuts] GPSDO control loops and correcting quantizationerror

Tom Knox actast at hotmail.com
Sun Sep 16 18:58:11 UTC 2012


Great dialog, One thing I have seen is the Allan intercept almost always has a "knee". If you wanted the best possible GPS quartz reference developing a variable Allan intercept would allow this knee to be moved and then mathematically removed during a gated measurement. 
Allowing to effectively see behind he knee offering lower uncertainty in this important area. 

Thomas Knox



> Date: Sun, 16 Sep 2012 19:20:24 +0200
> From: magnus at rubidium.dyndns.org
> To: time-nuts at febo.com
> Subject: Re: [time-nuts] GPSDO control loops and correcting quantizationerror
> 
> On 09/16/2012 05:47 PM, Poul-Henning Kamp wrote:
> > In message<5C52FBDBA5084AD4A36300FBA73BEF5E at pc52>, "Tom Van Baak" writes:
> >>> Yes, timing accuracy has been my main focus and in general I have been
> >>> using integration times on the low side of 10000 seconds for that,
> >>> but it depends a lot on the OCXO/Rb and environment.
> >>>
> >>> The PLL in NTPns is a (by now) old attempt to make a self-tuning PLL
> >>> for optimal time stability, and it does a surprisingly good job at it.
> >>
> >> Are there papers that talk about how to optimize for best timing or best
> >> frequency or (no free lunch) some compromise combination of the two?
> >
> > The only writings I am aware of, is what Dave Mills has written and
> > the PLL code in NTPns, but I havn't followed this closely in the last
> > 10 years, so do check for newer writings.
> >
> > Dave Mills coined the term "allan intercept" as the cross over of
> > the two sources allan variances and it's a good google search for
> > his relevant papers.
> >
> > I'm not entirely sure his rule of thumb for regulating to that point
> > is mathematically sound&  precise, but the concept itself is certainly
> > valid, even if you have to compensate for the timeconstant of the
> > PLL you use to regulate to that point.
> 
> Well, what is being used is phase-noise intercept. Conceptually a 
> similar intercept point will be available in Allan variance. However, as 
> you shift between noise-variants, the Allan (and Modified Allan) 
> variance has different scaling factor to the underlying phase noise 
> amplitudes. The danger of using the Allan variance variant is that you 
> get a bias in position compared to the phase-noise plots cross-overs.
> However, the concept is essentially the same, and the relative slopes is 
> the same. You get in the right neighbourhood thought.
> 
> The concept has been in use in the phasenoise world of things, so you 
> would need to search the phase-noise articles to find the real source. 
> It's been used to generate stable high-frequency signals.
> 
> The analysis of PLL based splicing of ADEV curves is tricky, and I have 
> not seen any good comprehensive analysis even if the general concept is 
> roughly understood. The equivalent on phase-noise is however well 
> understood and leaves no magic too it.
> 
> > I spent a lot of time with the code in NTPns, to try to get that PLL
> > to converge on the optimum, and while generally good, it's not perfect.
> >
> > The basic problem is that the data you have available for autotuning,
> > is the allan variance between your input and your steered source.
> 
> You need to treat the data as loose and tight PLL measure, depending on 
> what you look for. There is loads of calibration issues, covered in 
> literature.
> 
> > If you also have the allan variance between the steered source and
> > a 3rd, better, source, the task is pretty trivial:  Minimize the
> > area below that curve.
> >
> > But if you do that on the curve you have, you don't optimize, you
> > pessimize, since the lowest area, is with a timeconstant of zero.
> >
> > Going the other direction and maximizing the area is no good either
> > and trying to balance the area around some pivot related to the
> > present PLL timeconstant does not converge in my experience.
> >
> > What I did instead was to (badly) reinvent Shewarts ideas for testing
> > if the phase residual is under "statistical process control":
> >
> > I increase the timeconstant if the phase residual has too frequent
> > zero-crossings and loosen it if they happen too seldom.
> >
> > Having read a lot more about statistical process control, since I
> > built those NTP servers for the Air Traffic Control 10 years ago,
> > I would leverage more of the theory and heuristics developed in
> > process control. (3sigma violations, length of monotonic direction
> > etc. etc.)
> >
> 
> It's a complex field, and things like temperature dependencies helps to 
> confuse you.
> 
> Cheers,
> Magnus
> 
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