Re: NTP phase lock loop inputs and outputs?

Bruce <bmpenrod@xxxxxxxxxxx> writes:

The only thing that you can conclude from the referenced paper is that
for very short measurement intervals, order of a second, the noise
process is white phase. Obviously a simple average is optimal to
determine the time from a group of such closely spaced measurements.

It is not the time that is of interest in this discussion, it is the
frequency estimate. The frequency is estimated from the time measurements.
Mills claimed that there was no advantage to doing a least squares fit to
the sequence of time measurements, but that using only the end points was
always as good as a fit. I diputed that, and stated that IF the noise in
the time measuements was independent gaussian noise, fitting was always
better. If the noise is say 1/f noise (ie longer than the Allan minimum)
then there is no advantage I agree, but then using the endpoints is also
bad because, although you get a longer lever arm, you also get more noise
as well.


The paper then describes an algorithm to adapt to the decidedly
non-stationary measurement noise and local oscillator noise processes as
the averaging time is increased. Flicker and random walk of frequency
are mentioned, as well as white frequency. However he attributes this
to the crystal oscillator, which I believe is a mistake. Crystal
oscillators do not exhibit white frequency noise over longer averaging
times. If they did, we probably would not need Rubidium oscillators.

They do, but the flicker and random walk dominate if the time is long
enough.


All of these multiple noise processes operating simultaneously and
completely uncorrelated with each other are what make the precision time
transfer and frequency control art so interesting and allow so many
different ideas for how to best set the clock for the particular
application.

What is interesting about his comments is that doing a whole sequence of
very rapid time measurements and then long periods of quiet is better than
equally spacing the measurements. HOwever this would almost certainly
trigger the Kiss of Death and get the systems very upset with you. (eg make
10 measuments withing 2 sec say, and then wait for a day, rather than one
every couple of hours is better he would claim) But if a server running ntp
were hit with 10 rapid fire measurements from one machine would it
complain?



Bruce

Unruh wrote:
Bruce <bmpenrod@xxxxxxxxxxx> writes:

My understanding is that least squares is optimal only when the
residuals are white. For measurements of atomic frequency standards

Yes, and I clearly made that assumption. And the assumption is generally
true for short enough time intervals. If the netwrok delays are really
really short or if the time over which you are determining the frequency is
very long, then that is a bad assumption.


such as Rubidium or Cesium, the noise process is dominated by white
frequency noise, and in this case linear regression yields the optimal
estimate of frequency. A little snooping around on the NIST web site
will provide the relevant backup info.

For so many other precision timing and frequency applications, the noise
processes are decidedly un-white. David Allan developed his famous
two-sample variance to handle these divergent, non-stationary noise
processes. For instance, quartz oscillators are dominated by flicker
frequency noise for averaging times greater than about 100 milliseconds,
and eventually turn to random walk at longer averaging times. Selective
Availability of GPS (when it was in effect) was a white phase noise
process that modulated the time transfer for un-keyed users. The
statistics of network time transfer via ntp are undoubtedly divergent,
but I have not seen any data that showed it to be white frequency noise
dominant.

All the data suggests that it is white and the explicit assumption of that
Levine paper is that it is white.



So, it is not clear that linear regression is optimal for estimating the
frequency via ntp, unless someone has determined the statistics to be
white frequency. I personally have not performed the measurements to
make that determination, but it would not surprise me if Judah Levine has.

And he explicitly assumes that the network delay noise is white. His whole
procedure is to make a large ( eg 25-50) of ntp type measurements at one
time (withing seconds) then wait a long time ( 1/4 of a day) and doing it
again. He estimates teh frequency by averaging the measurements at any one
time, and then using that average phase error to determine the frequency.

The number of measurements at one instant is determined by requiring that
the frequency error due to the white noise ( decreases as sqrt(n)) is equal
to the other errors (flicker noise, etc) or equals the pre determined error
level wanted.




Bruce

Unruh wrote:
"David L. Mills" <mills@xxxxxxxx> writes:

Bill,
Read it again. Judah takes multiple samples to reduce the phase noise,
not to improve the frequency estimation.
Dave: The frequency estimate is done by subtracting two phase
determinations. Thus the phase noise enters the frequency determination. By
reducing the phase noise you reduce the frequency noise as well. I think
you need to read it again, but us just telling the other to read properly
will not help.

The frequency estimate is obtained in NTP and in his procedure by making
phase measurements.
f_i= (y_i-y_{i-1})/T
If y_i=z_i+e_i where z_i is the "true" time and e_i is a gaussian random
variable, then delta f_i= sqrt( <e_i^2>+<e_{i-1}^2>)/T
By reducing <e_i^2> you reduce delta f_i. And as you point out, you can
reduce <e_i^2> by making a bunch of measurements. Those measurements can be
all done at the end points or spread over the time interval T. The latter
is not quite as effective in reducing delta f_i since many of the
measurements do not have as long a "lever arm" as if they were all at the
endpoints, and that is why uniform sampling is about sqrt(3) worse than
clustering at the end points. But in either case, the more measurements you
make the more you reduce the uncertainty in the frequency estimate.

Anyway, at this point everyone else has enough information to make up their
own mind.



Dave
Unruh wrote:
You must have read a different paper than that one. I found it (through our
library) and it says that if you have n measurements in a time period T,
the best strategy is to take n/2 measurements at the beginning of the time
and n/2 at the end to minimize the effect of the white noise phase error on the
frequency estimate. That is perfectly true, and gives an error which goes
as sqrt(4/n)delta/T rather than sqrt(12/n)(delta/T) for equally spaced
measurements (assuming large n) T is the total time interval and delta is the std dev of each phase measurement . But it certainly does NOT say that if you have n
measurements, just use the first and last one to estimate the slope.

If you have n measurements, the best estimate of the slope is to do a least
squares fit. If they are equally spaced, the center third do not help much
(nor do they hinder), but a least squares fit is always the best thing to
do.


"David L. Mills" <mills@xxxxxxxx> writes:


Bill,
NIST doesn't agree with you. Only the first and last are truly
significant. Reference: Levine, J. Time synchronization over the
Internet using an adaptive frequency locked loop. IEEE Trans. UFFC,
46(4), 888-896, 1999.
Dave
Unruh wrote:
"David L. Mills" <mills@xxxxxxxx> writes:



Bill,
Ahem. The first point I made was that least-squares doesn't help the
frequency estimate. The next point you made is that least-squares
improves the phase estimate. The last point you made is that phase noise
No. The point I tried to make was the least squares improved the FREQUENCY
estimate by sqrt(n/6) for large n, where n is the number of points (assumed
equally spaced) at which the phase is measured. I am sorry that the way I
phrased it could have been misunderstood.


The phase is ALSO improved proportional to sqrt(n)
.
This assumes uncorrelated phase errors dominate the error budget.





is not important. Our points have been made and further discussion would
be boring.
Except you misunderstood my point. It may still be boring to you.




Dave
Unruh wrote:


"David L. Mills" <mills@xxxxxxxx> writes:




Bill,
If you need only the frequency, least-squares doesn't help a lot; all
you need are the first and last points during the measurement interval.
Well, no. If you have random phase noise, a least squares fit will improve
the above estimate by roughly sqrt(n/4) where n is the number of points.
That can be significant. It is certainly true that the end points have the
most weight ( which is why the factor of 1/4). Ie, if you have 64 points,
you are better by about a factor of 4 which is not insignificant.




The NIST LOCKCLOCK and nptd FLL disciplines compute the frequency
directly and exponentially average successive intervals. The NTP
discipline is in fact a hybrid PLL/FLL where the PLL dominates below the
Allan intercept and FLL above it and also when started without a
frequency file. The trick is to separate the phase component from the
frequency component, which requires some delicate computations. This
allows the frequency to be accurately computed as above, yet allows a
phase correction during the measurement interval.
He of course is not interested in phase corrections.






Dave
Unruh wrote:



David Woolley <david@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> writes:





Unruh wrote:
I do not understand this. You seem to be measuring the offsets, not the
frequencies. The offset is irrelevant. What you want to do is to measure
Measuring phase error to control frequency is pretty much THE standard
way of doing it in modern electronics. It's called a phase locked loop
Sure. In the case of ntp you want to have zero phase error. ntp reduces the
phase error slowly by changing the frequency. This has the advantage that
the frequency error also gets reduced (slowly). He wants to reduce the
frequency error only. He does not give a damn about the phase error
apparently. Thus you do NOT want to reduce the frequecy error by attacking
the phase error. That is a slow way of doing it. You want to estimate the
frequency error directly. Now in his case he is doing so by measuring the
phase, so you need at least two phase measurements to estimate the
frequency error. But you do NOT want to reduce the frequency error by
reducing the phase error-- far too slow.

One way of reducing the frequency error is to use the ntp procedure but
applied to the frequency. But you must feed in an estimate of the frequecy
error. Anothr way is the chrony technique. -- collect phase points, do a
least squares fit to find the frequency, and then use that information to
drive the frequecy to zero. To reuse past data, also correct the prior
phase measurements by the change in frequency.
(t_{i-j}-=(t_{i}-t_{i-j}) df





(PLL) and it is getting difficult to find any piece of electrnics that
doesn't include one these days. E.g. the typical digitally tuned radio
A PLL is a dirt simply thing to impliment electronically. A few resistors
and capacitors. It however is a very simply Markovian process. There is far
more information in the data than that, and digititally it is easy to
impliment far more complex feedback loops than that.






or TV has a crystal oscillator, which is divided down to the channel
spacing or a sub-multiple, and a configurable divider on the local
oscillator divides that down to the same frequency. The resulting two
signals are then phase locked, by measuring the phase error on each
cycle, low pass filtering it, and using it to control the local
oscillator frequency, resulting in their matching in frequency, and
having some constant phase error.
the offset twice, and ask if the difference is constant or not. Ie, th
eoffset does not correspond to being off by 5Hz.
ntpd only uses this method on a cold start, to get the initial coarse
calibration. Typical electronic implementations don't use it at all,
but either do a frequency sweep or simply open up the low pass filter,
to get initial lock.
And? You are claiming that that is efficient or easy? I would claim the
latter. And his requirements are NOT ntp's requirements. He does not care
about the phase errors. He is onlyconcerned about the frequency errors.
driving the frequency errors to zero by driving the phase errors to zero is
not a very efficient technique-- unless of course you want the phase errors
to be zero( as ntp does, and he does not).




.

Relevant Pages

  • Re: NTP phase lock loop inputs and outputs?
    ... The bottom line is that in most real-world NTP configurations for WANs the real enemy is not phase noise, but frequency noise with H parameters considerably greater than 0.5. ... For measurements of atomic frequency standards such as Rubidium or Cesium, the noise process is dominated by white frequency noise, and in this case linear regression yields the optimal estimate of frequency. ...
    (comp.protocols.time.ntp)
  • Re: NTP phase lock loop inputs and outputs?
    ... NTP measurements are in my book. ... noise, but frequency noise with H parameters considerably greater than 0.5. ... YOu have NOT been hollering about the Allan intercept. ...
    (comp.protocols.time.ntp)
  • Re: NTP phase lock loop inputs and outputs?
    ... that phase noise and frequency noise ... determine the time from a group of such closely spaced measurements. ... non-stationary measurement noise and local oscillator noise processes as ... The statistics of network time transfer via ntp are ...
    (comp.protocols.time.ntp)
  • Re: NTP phase lock loop inputs and outputs?
    ... The only thing that you can conclude from the referenced paper is that for very short measurement intervals, order of a second, the noise process is white phase. ... Obviously a simple average is optimal to determine the time from a group of such closely spaced measurements. ... The paper then describes an algorithm to adapt to the decidedly non-stationary measurement noise and local oscillator noise processes as the averaging time is increased. ... The statistics of network time transfer via ntp are undoubtedly divergent, but I have not seen any data that showed it to be white frequency noise dominant. ...
    (comp.protocols.time.ntp)
  • Re: NTP phase lock loop inputs and outputs?
    ... Judah and I have come around the issue of white/flicker frequency noise with cold rocks (grotty computer oscillators). ... I found with careful technique, as documented in previous papers and my book, that phase noise and frequency noise characteristics of cold rocks are generally separable, mainly because the flicker noise is so bad. ... Obviously a simple average is optimal to determine the time from a group of such closely spaced measurements. ... The statistics of network time transfer via ntp are undoubtedly divergent, but I have not seen any data that showed it to be white frequency noise dominant. ...
    (comp.protocols.time.ntp)