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
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