[time-nuts] New Subscriber, DIY GPSDO project (yes, another one)

[Magnus Danielson]

Hi,

On 2020-03-10 12:53, Attila Kinali wrote:
> On Tue, 10 Mar 2020 03:38:11 +0100
> Magnus Danielson <magnus at rubidium.se> wrote:
>
>> Now, to raise the complexity, the state-model of noise does not allow
>> for flicker noise variants. There just isn't a a good way to express
>> that. There is a few articles that give rough estimates, but no
>> half-integrators to be seen and therefore the noise models which is so
>> important in Kalman does not work very well.
> There is a thing called "fractional control" which deals with fractional
> order (integrator/differentiator) control loops. But, what I have seen
> so far was only fractional order in the underlying system model, not in
> the noise. But I have only scratched at the surface of this topic, so
> there is a lot I have not seen yet.
>
> If someone here knows more about fractional control, I would really
> enjoy a chat about the topic.

Yes, but the base point is that it's not off the shelf standard Kalman.
The noise covariance matrix may be sufficient, but I have not been
convinced. Traditional Kalman only speak about white noise, which in our
context becomes white phase modulation noise, but the actual model for
noise uses a co-variance matrix and it becomes trivial to extend it to
white frequency modulation noise, as it would be the noise for the
frequency state. This white frequency modulation noise is not spoken
much of  in traditional literature, but actually fits the model as one
builds a phase/frequency Kalman model. However, a noise model has at
least two more fractional states, but the state model does not, and
expressing that in Kalman matrixes is tricky to say the least. I've seen
some papers touch on the subject, but I have not been convinced on their
approach for the fractional noises.

Cheers,
Magnus