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

[Bob kb8tq]

Hi

Three corner hat can fail for a variety of reasons. If all the data is
done in a simultaneous fashion then the most likely is that indeed
one source is way better than the others over some span of Tau’s . 

If that’s the case, then the only real answer is to come up with some
better sources as references. There are other ways it can go wrong so,
you can never be 100% sure it comes from this or that source. 

Bob

> On Oct 15, 2022, at 7:47 AM, Erik Kaashoek via time-nuts <time-nuts at lists.febo.com> 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-02  1.089e-10  3.416e-11  2.631e-11
> 6.400e-02  1.235e-10  3.859e-11  2.168e-11
> 1.280e-01  1.382e-10  3.659e-11  2.083e-11
> 2.560e-01  1.538e-10  5.818e-11  Negative
> 5.120e-01  1.718e-10  5.025e-11  Negative
> 1.024e+00  1.745e-10  5.221e-11  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
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