[time-nuts] Re: ADEV on data with gaps

[Michael Wouters]

Hello Jim

"At a first glance, it seems that the calculation for each tau will have
a different number of measurements contributing.  Say I have 1000
seconds of data, once a second, and there's a gap of 100 seconds
somewhere in the middle.  For the 1 second tau, I've got 900
measurements.  for a 100 second tau, I'll have 800 ..."

That's the right idea - you just skip the differences y_k+1 - y_k
where there are missing points, so you end up with fewer points at
each averaging time
There are various papers that describe the bias in ADEV etc that this
introduces.

Stable32 deals with gaps
http://www.wriley.com/Gaps.htm

If python is your thing, allantools does too.

Otherwise there are MATLAB tools too
https://github.com/groundstate/tftools

Cheers
Michael

On Sat, Aug 5, 2023 at 6:11 AM Lux, Jim via time-nuts
<time-nuts at lists.febo.com> wrote:
>
> I've got a series of clock measurements where the actual measurement
> occasionally has problems (e.g. it's measured against GPS, and there are
> GPS partial outages).
>
> What's a strategy for calculating ADEV (and related parameters) where
> there are data in the sequence that are excised? For example, does
> Timelab or Stable32 have a way to have timestamps for the
> frequency/phase measurements that recognizes gaps?
>
> At a first glance, it seems that the calculation for each tau will have
> a different number of measurements contributing.  Say I have 1000
> seconds of data, once a second, and there's a gap of 100 seconds
> somewhere in the middle.  For the 1 second tau, I've got 900
> measurements.  for a 100 second tau, I'll have 800 measurements (because
> for 200, one or the other end point is missing), etc.
>
> Some plots attached showing some data.  In this case, I'm looking at a
> post calculated "clock bias" between GPS and the clock - that is,
> there's a process that estimates the clock offset (in meters). A first
> difference gets rate, and clock has some relatively fixed bias (that
> changes with time), and random variations on top of that.  However, the
> measurement depends on the SNR of the GPS signals (lower plot on
> biasdrift, it's the measurement uncertainty estimate)
>
> At some point, of course, the ADEV measurement is limited by the GPS
> measurement uncertainty - if it's 1 ns, then ADEV is never going to
> measure less than 1E-9 over 1 second.
>
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