[time-nuts] suitable statistics for measurements with gaps

Magnus Danielson magnus at rubidium.dyndns.org
Sat Apr 23 22:36:38 UTC 2016


Hi Jim,

On 04/22/2016 03:39 PM, jimlux wrote:
> All woodpecker kidding aside, this brings up an interesting question.
>
> For most of the measures we look at: ADEV and related measures, you're
> looking at statistics collected essentially continuously (e.g. adjacent
> sample frequency) at various time offsets.
>
> But what about when the observations have gaps? Say you're measuring the
> frequency of a spacecraft oscillator, and you can only see it for 8
> hours a day?  the description of the frequency variation at a time
> difference of 24 hours is useful, even if the integration time for each
> measurement is, say, 1000 seconds.

In general, you can build your ADEV for any tau where you have three 
samples in a row with tau seconds inbetween. You will need to account 
for how many values you accumulate for each tau, and that will be 
different from that of normal full set of samples, in order to properly 
estimate the degrees of freedom and hence confidence intervals.
There will be ranges of tau for which no squares can be accumulated, but 
others can get more. Doing it this way can help you. There will be jumps 
in the plot, but other than that it will be OK.

> Maybe such things are so idiosyncratic that the description should be
> unique to the situation, or maybe there's no real insight to be gained
> by a generalized formulation, as there is with the Leeson model.

Judge for yourself, but you can continue the ADEV plot out to longer 
times and estimate the slopes over the gaps in the tau-plot.

Similarly can least square measures of phase and frequency be done based 
on data with gaps, a recent presentation and paper from yours truly 
raised that as a question and I realized that it was indeed quite easy 
to do. Can be discussed at IFCS.

Cheers,
Magnus



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