[time-nuts] Re: GPSDO Control loop autotuning

[Magnus Danielson]

Hi Matthias,

On 2022-04-21 23:20, Matthias Welwarsky wrote:
> On Dienstag, 12. April 2022 00:52:42 CEST Magnus Danielson via time-nuts
> wrote:
>
>> A trivial state-space Kalman would have phase and frequency. Assuming
>> you can estimate the phase and frequency noise of both the incoming
>> signal and the steered oscillator, it's a trivial exercise. It's
>> recommended to befriend oneself with Kalman filters as a student
>> exercise. It can do fairly well in various applications.
> I'm wondering, can the frequency really be part of the state? It is not a
> property we can measure independently, we can only derive it from the TIC
> measurements. There is the EFC value of course, but that doesn't directly
> correspond with the output frequency...

You confuse state with observability. It is true that you make the 
observation in phase, but the system matrix include that the estimated 
frequency updates the phase

phase = phase + frequency * delta_t

frequency = frequency

So matrix becomes

[1 delta_t]

[0 1]

for a [phase frequency]^T state vector in and out.

With such a system matrix, the Kalman filter when stabilize degenerate 
to a PI-loop system, which is what was concluded again in a mail just 
recently, they get same performance.

It works.

Not, you should make models for the noise of the reference and for the 
local oscillator. This is used to update the estimated uncertainty of 
the states, but this is where flicker noise-types does not work well, 
and all you can expect is approximations. This was also concluded again 
in a separate email.

Kalman is a nice tool, but does not bite very well on flicker noise. You 
could potentially get it better by attemping to filter the noise to be 
whiter, but it does not really work well. Kalman is not well adapted to 
this problem, but form a nice alternative to PI when it comes to 
avoiding heuristics to step PI loop bandwidth.

Cheers,
Magnus