Re: NTP phase lock loop inputs and outputs?
- From: Unruh <unruh-spam@xxxxxxxxxxxxxx>
- Date: Sun, 01 Jun 2008 18:58:14 GMT
"David L. Mills" <mills@xxxxxxxx> writes:
Bruce,
Judah and I have come around the issue of white/flicker frequency noise
What does this sentence mean? Does it mean you have come around to the same
viewpoint, or that you are still arguing about it.
with cold rocks (grotty computer oscillators). Determining accurate
Exactly why you would call them "cold rocks" and then use them as though
they meant something to anyone else I do not know.
Allan deviation plots is something of a black art and at hazard to
insiduous resonances. 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. Therefore, the intersection of the phase
I assume by flicker noise you mean 1/f noise.
characteristic and frequency characteristic is generally well defined,
which I call the Allan intercept. This is why the NTP discipline is
mainly responsive to phase noise below the intercept and frequency noise
above.
Except that the Allan intercept depends on a whole bunch of things,
including the noise in the measurement process ( network delays and noise
for example). There is no single Allan intercept. It depends on the system.
The Allan intercept can be minutes or days depending even on exactly the
same computer.
Also as Levine says and my measuements confirm, on the timescale of a few hours, it is the daily temp
variations, not flicker noise or any other semi Markovian process (ie
uncorrelated noise in the frequency domain) that dominates. Computers tend
to get used during the day, and thus heat up during the day, and not at
night. One would like an adaptive process which tries to measure the
current Allan or equivalent (ie is the frequency noise due to the white
measurement noise or is it more correlated) rather than relying on some
"average" intercept.
I would note that chrony has an algorithm to try to do just that-- by
estimating whetehr or not a least squares linear fit to the phase errors is
a reasonable statistical estimate or whether the measurements indicate that
this model is failing. Ie, it tries to dynamically adapt to the actual
noise type.
Dave
Bruce wrote:
.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. 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.
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.
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).
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