[palebluedot]

> All of these were well covered by state estimation research from 80s to now, but again, the textbooks seem to be written in stone in 1972.

Do you have any good resources (online or textbook) you could recommend, as an introduction to these concepts, that is more modern / up-to-date?

[jvanderbot]

I don't, sadly. The only coverage of this that was first-principles accessible was the course taught by Prof Stergios Romelioutis where I went to grad school.

You could do fine by reading some old books by Bar-Shalom. Any practical textbook like his would include all the "other stuff" about the EKF that helps you understand how nonperforming it often is.

But the actual derivation of the EKF is probably only one or two pages in such a textbook, which is a damn shame nobody includes it.

The background required is simply:

* Know the form of exponential family of PDFs (like Normal Gaussian)

* Bayes rule

* Recognize that to maximize f~= exp(-a), you have to minimize 'a'

* Know how to take derivative of matrix equation ('a', above)

* Solve it

* Use 'matrix inversion lemma' to transform solution to what KF/EKF provides.

Ah hell, I'll just write it up.

[markisus]

Probabilistic Robotics covers Kalman Filter from a first principles probabilistic viewpoint, and its extension the EKF. It's quite readable for someone with basic understanding of linear algebra, probability, and calculus. I believe it also has a refresher on these basics in the introduction.

http://www.probabilistic-robotics.org/