[time-nuts] Modified Allan Deviation and counter averaging

[Magnus Danielson]

Poul-Henning,

On 08/03/2015 01:07 AM, Poul-Henning Kamp wrote:
> --------
> In message <55BDB002.8060408 at rubidium.dyndns.org>, Magnus Danielson writes:
>
>> For true white PM *random* noise you can move your phase samples around,
>> but you gain nothing by bursting them.
>
> I gain nothing mathematically, but in practical terms it would be
> a lot more manageable to record an average of 1000 measurements
> once per second, than 1000 measurements every second.

Yes, averaging them in blocks and only send the block result is indeed a 
good thing, as long as we can establish the behavior and avoid or remove 
any biases introduced. Bursting them in itself does not give much gain, 
as the processing needs to be done anyway and even rate works just as 
well. A benefit of a small burstiness is that you can work on beat-notes 
not being multiple of the tau0 you want, say 1 s.

As in any processing, cycle-unwrapping needs to be done, as it would 
waste the benefit.

For random noise, the effect of the burst or indeed aggregate into 
blocks of samples is just the same as doing overlapping processing as 
was done for ADEV in the early 70thies as a first step towards better 
confidence intervals. For white noise, there is no correlation between 
any samples, so you can sample them at random. However, for ADEV the 
point is to analyze this for a particular observation interval, so for 
each measure being squared, the observation interval needs to be 
respected. For the colored noises, there is a correlation between the 
samples, and it is the correlation of the observation interval that main 
filtering mechanism of the ADEV. However, since the underlying source is 
noise, you can use any set of phase-tripplets to add to the accumulated 
variance. The burst or block average, provides such a overlapping 
processing mechanism.

However, for systematic noise such as the counter's first order time 
quantization (thus ignoring any fine-grained variations) will interact 
in different ways with burst-sampling depending on the burst length. 
This is the part we should look at to see how we best achieve a 
reduction of that noise in order to quicker reach the actual signal and 
reference noise.

>> For any other form of random
>> noise and for the systematic noise, you alter the total filtering
>> behavior [...]
>
> Agreed.

I wonder if not the filter properties of the burst average is altered 
compared to an evenly spread block, such that when treated as MDEV 
measures we have a difference. The burst filter-properties should be 
similar to that of PWM over the burst repetition rate.

I just contradicted myself. I will come back to this topic, one has to 
be careful as filter properties will color the result and biases can 
occur. Most of these biases is usually not very useful, but the MDEV 
averaging is, if used correctly.

Cheers,
Magnus