[time-nuts] Re: 3-Cornered Hat fails with negative variances, is there anything I can to to improve?

[Magnus Danielson]

Hi Erik,

The basic problem is that averaging does not happen before the squaring. 
The Grosslambert solves this similar to cross-correlation to average 
before being squared into power, which is needed to avoid the negative 
results in the three-cornered hat. As we measure between two sources, 
the noise power of both sources contributed to the added noise power, so 
one need to sort the balance out in power domain, but the trouble is 
that the noise levels only cancel in the amplitude domain, and for ADEV 
this is not where it excels.

Cheers,
Magnus

On 2022-10-16 07:55, Erik Kaashoek via time-nuts wrote:
> Hi Magnus,
> Thanks, will try a longer measurement.
> As I can do simultaneous absolute phase relation measurement of 3 
> sources  (Phase A vs B, B vs C, C vs A), is there a way to not use the 
> phase variance but a more direct relation?
> I may be able to calculate A,B and C directly from the 3 equations at 
> every Tau.
> This would hide a common noise component but after some time this 
> noise should cancel out, I hope
> Erik
>
>
> On 16-10-2022 1:11, Magnus Danielson via time-nuts wrote:
>> There is a built-in weakness into 3-cornered hat that achieves this 
>> and it is only when you have long measurs that it tends to resolve 
>> itself. Some research being done suggest that Grosslambert processing 
>> avoids it, but it is not off the shelf processing but what is 
>> recommended in latest revision of IEEE Std 1039 do use for the 
>> situation.
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