Hi, On 2020-03-10 00:46, jimlux wrote: > On 3/9/20 2:36 PM, Poul-Henning Kamp wrote: >> -------- >> In message <3899483.rfyw6ut...@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 _______________________________________________ time-nuts mailing list -- time-nuts@lists.febo.com To unsubscribe, go to http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com and follow the instructions there.