3-Cornered Hat fails with negative variances, is there anything I can to to improve?
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
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@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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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-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
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
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.
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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