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

[Magnus Danielson]

Hi,

On 2020-03-10 00:46, jimlux wrote:
> On 3/9/20 2:36 PM, Poul-Henning Kamp wrote:
>> --------
>> In message <3899483.RfYW6UTW6g at linux-5fgm.suse>, Matthias Welwarsky
>> writes:
>>
>>> I've actually been thinking of using a Kalman filter to find the
>>> "true value"
>>> of the EFC. I just couldn't wrap my mind around the theory yet.
>>
>> Yeah, they are hard to get started with, there seems to be only two
>> kinds of texts about Kalman: Hard-core math and woo-doo library usage.
>>
>
> Kalman filters are actually pretty simple..
> They're basically a single exponential type smoothing filter y(i) =
> alpha * x(i) + (1-alpha)*y(i-1)
>
> where you choose alpha to be related to the current uncertainty of the
> estimate and the uncertainty of the measurement, so that each
> contributes such that the new estimate has the minimum uncertainty.
>
> Where it gets tricky is when you have multiple variables in and out,
> and you need to have the covariances of the inputs to be able to
> "choose wisely"
>
> And, since in most implementations, the multiple variables are the
> state variables (x(t), x'(t), x''(t), etc). the uncertainty in the
> measurements of the higher derivatives tends to be higher (because a
> differentiator is a high pass filter).

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.

The covariance matrixes may be given some semi-relevant form thought,
but nothing have been very straight that I have seen.

It should be said that Kalman is kind of optimum for "white" noise
(what-ever that is), but we are far from white noise. Variants of Kalman
filters use noise-colour compensation of some sort, and that kind of
solves some of the issues. It does not fit the problem perfectly. This
is why time-scale algorithms is not directly Kalman filters but only
Kalman-esque to some degree.

Cheers,
Magnus