Re: [time-nuts] generalization of three cornered hat

[Forrest Christian (List Account)]

I apologize if the following isn't helpful.   I'm still getting my
head around all of the details of statistical analysis of clocks so
I'm not 100% sure this matches what you're asking for, but I figured
it might be helpful so...

A portion of the document at https://tf.nist.gov/general/pdf/1288.pdf
might be helpful. In Section XV on the page labeled 2588 and
subsequent pages it describes the AT1 algorithm which is used by NIST
to mathematically combine N clocks into a single Virtual Ensemble
clock using averaging and weighting of the clocks.   As a side effect
the algorithm provides a method to determine the quality of each clock
for the purpose of increasing or decreasing the weight each clock is
given when computing the Ensemble clock.  Not sure if this matches
your needs, but it seems like it might be close.

In searching for the above document I also found
http://www.nict.go.jp/publication/shuppan/kihou-journal/journal-vol50no1.2/0501.pdf
which contains summaries not only of AT1 but also other algorithms.

On Sat, Jun 15, 2019 at 5:08 PM jimlux  wrote:
>
> I found a lot of references to estimating the uncertainties in
> measurements derived with three cornered hat.   What about for arbitrary
> N sources and N(N-1)/2 pair-wise measurements?  There must be some magic
> term to search for.
>
>
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-- 
- Forrest

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Re: [time-nuts] generalization of three cornered hat

[jimlux]

On 6/16/19 4:22 AM, Poul-Henning Kamp wrote:





Note that when you consider transitive measurement noise, you may find
that making N simultaneous measurements against a single independent LO
is simpler and better than making N(N-1)/2 measurements of all possible
clock pairs. Think of star vs. ring vs. mesh networks.


I think there is a fundamental assumption that needs to be stated clearly here:

3-cornered hat and it's extensions are only productive with homogenous,
and preferably identical, sources.  Ie: 3 identical OCXO's, 3 HP5071As.

If you do a 3CH on a raw GPS-PPS, an Rb and a H-maser, you get a really
shitty result, because it attributes the worst properties of each source
to the "virtual source".

For heterogenous sources, pretty much all proposed time-scale
algorithms degenerate to 1st or 2nd order PLLs with suitably chosen
parameters and filters.

Arguably, the most important property of any timescale algorithm
is the ability to alert and exclude false-tickers as early as
possible, which makes Kalman filters obvious, despite their quirks.




The Torcaso paper will get me started, and some of the helpful search terms.
What I'm looking for is the mathematical formalism to estimate the 
uncertainty of each individual source, given pair-wise (or many to one) 
measurements, each with some uncertainty of their own.


The 3 pairwise measurements is a standard technique for measuring the 
gain (or loss) of antennas or waveguide connections, for instance.


I'm sure there's some standardized statistical approach here - perhaps 
one builds a large estimated covariance matrix. (essentially what a 
Kalman filter winds up using, with the covariance either known a-priori, 
or estimated on the fly)


There's apparently a variety of Least Squares algorithms... Mobile 
Generalized Least Squares (MGLS)






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Re: [time-nuts] generalization of three cornered hat

[Bob kb8tq]

Hi

…….. and if you want to dig into ensembles of “non similar” clocks, you want to 
look into
David Allan’s Smart Clock stuff….

http://www.allanstime.com/Publications/DWA/ 


There’s also a lot of stuff there on clock ensembles in general. 

Bob

> On Jun 16, 2019, at 7:22 AM, Poul-Henning Kamp  wrote:
> 
> 
> 
> 
>> Note that when you consider transitive measurement noise, you may find 
>> that making N simultaneous measurements against a single independent LO 
>> is simpler and better than making N(N-1)/2 measurements of all possible 
>> clock pairs. Think of star vs. ring vs. mesh networks.
> 
> I think there is a fundamental assumption that needs to be stated clearly 
> here:
> 
> 3-cornered hat and it's extensions are only productive with homogenous,
> and preferably identical, sources.  Ie: 3 identical OCXO's, 3 HP5071As.
> 
> If you do a 3CH on a raw GPS-PPS, an Rb and a H-maser, you get a really
> shitty result, because it attributes the worst properties of each source
> to the "virtual source".
> 
> For heterogenous sources, pretty much all proposed time-scale
> algorithms degenerate to 1st or 2nd order PLLs with suitably chosen
> parameters and filters.
> 
> Arguably, the most important property of any timescale algorithm
> is the ability to alert and exclude false-tickers as early as
> possible, which makes Kalman filters obvious, despite their quirks.
> 
> -- 
> Poul-Henning Kamp   | UNIX since Zilog Zeus 3.20
> p...@freebsd.org | TCP/IP since RFC 956
> FreeBSD committer   | BSD since 4.3-tahoe
> Never attribute to malice what can adequately be explained by incompetence.
> 
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> time-nuts mailing list -- time-nuts@lists.febo.com
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Re: [time-nuts] generalization of three cornered hat

[Poul-Henning Kamp]

>Note that when you consider transitive measurement noise, you may find 
>that making N simultaneous measurements against a single independent LO 
>is simpler and better than making N(N-1)/2 measurements of all possible 
>clock pairs. Think of star vs. ring vs. mesh networks.

I think there is a fundamental assumption that needs to be stated clearly here:

3-cornered hat and it's extensions are only productive with homogenous,
and preferably identical, sources.  Ie: 3 identical OCXO's, 3 HP5071As.

If you do a 3CH on a raw GPS-PPS, an Rb and a H-maser, you get a really
shitty result, because it attributes the worst properties of each source
to the "virtual source".

For heterogenous sources, pretty much all proposed time-scale
algorithms degenerate to 1st or 2nd order PLLs with suitably chosen
parameters and filters.

Arguably, the most important property of any timescale algorithm
is the ability to alert and exclude false-tickers as early as
possible, which makes Kalman filters obvious, despite their quirks.

-- 
Poul-Henning Kamp   | UNIX since Zilog Zeus 3.20
p...@freebsd.org | TCP/IP since RFC 956
FreeBSD committer   | BSD since 4.3-tahoe
Never attribute to malice what can adequately be explained by incompetence.

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Re: [time-nuts] generalization of three cornered hat

[Tom Van Baak]

Jim,

With N oscillators involved: look for papers about clock ensembles and 
time scale algorithms.


The 3 corner hat method, where you create a fictitious mean of 3 clocks 
and then compute the deviation of each real clock from the virtual mean, 
is just like a simple unweighted 3-clock time scale. And that can be 
extended far beyond N=3. For example, think of how most national time 
labs handle their many Cs clocks, or how UTC itself is computed.


Note that when you consider transitive measurement noise, you may find 
that making N simultaneous measurements against a single independent LO 
is simpler and better than making N(N-1)/2 measurements of all possible 
clock pairs. Think of star vs. ring vs. mesh networks.


/tvb


On 6/15/2019 3:54 PM, jimlux wrote:
I found a lot of references to estimating the uncertainties in 
measurements derived with three cornered hat.   What about for 
arbitrary N sources and N(N-1)/2 pair-wise measurements?  There must 
be some magic term to search for.



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Re: [time-nuts] generalization of three cornered hat

[Bruce Griffiths]

Try:
https://www.researchgate.net/publication/235103340_Estimating_Frequency_Stability_and_Cross-Correlations

Bruce
> On 16 June 2019 at 10:54 jimlux  wrote:
> 
> 
> I found a lot of references to estimating the uncertainties in 
> measurements derived with three cornered hat.   What about for arbitrary 
> N sources and N(N-1)/2 pair-wise measurements?  There must be some magic 
> term to search for.
> 
> 
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> time-nuts mailing list -- time-nuts@lists.febo.com
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> http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com
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[time-nuts] generalization of three cornered hat

[jimlux]

I found a lot of references to estimating the uncertainties in 
measurements derived with three cornered hat.   What about for arbitrary 
N sources and N(N-1)/2 pair-wise measurements?  There must be some magic 
term to search for.



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