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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