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.

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.

Dave

Unruh wrote:[color=blue]

> David Woolley <david@ex.djwhome.demon.co.uk.invalid> writes:

>

>[color=green]

>>Unruh wrote:[/color]

>

>[color=green][color=darkred]

>>>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[/color][/color]

>

>[color=green]

>>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[/color]

>

>

> 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

>

>[color=green]

>>(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[/color]

>

>

> 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.

>

>

>[color=green]

>>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.[/color]

>

>[color=green][color=darkred]

>>>the offset twice, and ask if the difference is constant or not. Ie, th

>>>eoffset does not correspond to being off by 5Hz.[/color][/color]

>

>[color=green]

>>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.[/color]

>

>

> 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).

>

>

>

>[/color]