"David L. Mills" <[EMAIL PROTECTED]> 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" <[EMAIL PROTECTED]> 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" <[EMAIL PROTECTED]> 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" <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]> 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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