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

[jimlux]

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).


A Maximum Likelihood LMS estimator is essentially a special case of a 
Kalman filter.

And, of course, because no modern discussion is complete without working 
in Machine Learning: the classic LMS adjustment methods(w(i+1) = w(i) + 
alpha * x(i)) for a single layer classifier boils down to the same thing.