[time-nuts] Re: Timestamping counter techniques : phase computation question

[Magnus Danielson]

Erik,

On 2022-01-31 22:17, Erik Kaashoek wrote:
> @Magnus
> The time interval of the capturing of the counters is not always exactly
> the same. There could be even substantial variation if the capture interval
> is close to the event interval. Is this a problem for the calculation
> method you propose?

Observant!

Yes, so there is an assumption that the time between samples is robust. 
In fact, this an approximation assumed that there is a regular \tau_0 
for each sample, and with that you can collapse the big linear algebra part.

At the same time, as you slip one cycle of the signal and measures the 
edge of a later cycle (thus having an event count higher than ideal), 
the next measure event will be one cycle shorter as it is likely to 
occurr on that ideal event. These tend to balance out. If you do plain 
averaging, it turns out the balance out perfectly, because as you add 
the time and event you just expanded the base-length. This is why just 
plain averaging does not give you more precision than just measure the 
end-points. Now, if you make separate frequency estimates and average 
those, it will not perfectly balance but the effect would be fairly small.

So, if your time-base generator is not stable, it can help to polute 
your observations somewhat. To some degree this can be remedied by 
running a separate least square on the on the event data to produce a 
\tau_0 estimate and plug into the final estimator forms. Another 
approach is to make sure that the time-base is just a certain number of 
cycles of event or time counter.

An approach to slipped cycles is to back-annotate them, simply by 
removal of their phase advance over that time. If your frequency is very 
near perfect match-up, that impact will be very low anyway so it can be 
ignored. Actually, it is usually ignored.

So, you just stumbled on one of the more peculiar things that make 
counter frequency estimation less perfect that you would think, part of 
it's systematic noise. A systematic noise often being overlooked and 
ignored. Funny is, some of it washed out with white noise and averaging.

Cheers,
Magnus