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

[Magnus Danielson]

Hi Erik,

On 2022-10-15 13:47, Erik Kaashoek via time-nuts wrote:
> After measuring and calculating the ADEV of three oscillators [1] the 
> TAU files where created using Stable32 and the 3 TAU files where used 
> to performed a 3-Cornered Hat variance analysis with this result:
>
> 3-Cornered Hat Separation of Variances
> A-B Stability Data: RbvsRg.TAU
> A-C Stability Data: OCXOvsRG.TAU
> B-C Stability Data: OCXOvsRb.TAU
>    Tau       Sigma A    Sigma B    Sigma C
> 2.000e-03  5.784e-10  Negative   4.732e-10
> 4.000e-03  2.957e-10  Negative   2.267e-10
> 8.000e-03  1.640e-10  Negative   1.123e-10
> 1.600e-02  1.096e-10  Negative   5.694e-11
> 3.200e-02Â  1.089e-10Â  3.416e-11Â  2.631e-11
> 6.400e-02Â  1.235e-10Â  3.859e-11Â  2.168e-11
> 1.280e-01Â  1.382e-10Â  3.659e-11Â  2.083e-11
> 2.560e-01Â  1.538e-10Â  5.818e-11Â  Negative
> 5.120e-01Â  1.718e-10Â  5.025e-11Â  Negative
> 1.024e+00Â  1.745e-10Â  5.221e-11Â  Negative
> 2.048e+00  1.822e-10  Negative   7.644e-11
> 4.096e+00  1.685e-10  Negative   7.813e-11
> 8.192e+00  1.519e-10  Negative   8.429e-11
> 1.638e+01  1.523e-10  Negative   8.295e-11
>
> As far as I understand the negative variances are because the 
> calculation method fails.
> The method did calculate the variance for the least stable source (A)
>
> Am I correct to assume the difference between B and C is too small for 
> this method to separate their contribution?
> Or is there anything I can/should to to separate B and C
>
> [1] http://athome.kaashoek.com/time-nuts/DMTD/3-hat_input.png

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. Search for Francois 
Vernotte on that topic. Prof. Vernotte was one of the reviewers on Dr. 
Kinalis thesis earlier this week, for very good reasons. Prof. Vernotte 
earns my deepest respect in this field.

Cheers,
Magnus