[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)