"David L. Mills"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 Woolleywrites:

>>

>>

>>>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).

>>

>>

>>

>>