Kalman filters

eddyc

Hi, as part of my research I am trying to understand the workings of Kalman Filters. Unfortunately I am finding the mathematics involved extremely difficult to understand. I have a basic understanding of DSP and I am a half decent programmer. I was just wondering what particular areas of mathematics I should look at to help me understand how Kalman filters work. I am currently working through the Stroud Engineering Mathematics book, but I haven't found anything directly related to this area in it. Thanks.

Michael Collins

Can you post an example of the maths you've come across so far in relation to Kalman filters that you found difficult?

I suspect some probability and general linear system theory would be quite useful. If you want to really grasp the field, I'd suggest starting with Introduction to Digital Filters by J. O. Smith - one of the best, and most self contained, books available, in my opinion. Here's the online version (if you think it's suitable I'd recommend getting the hardcopy from Amazon).

https://ccrma.stanford.edu/~jos/filters/

If the maths in that is tough, you could always read the first few chapters of Mathematics of the DFT by the same author. Here's the online version of this one:

https://ccrma.stanford.edu/~jos/mdft/

eddyc

My mathematics education really only goes as far as introduction to Calculus, my algebra is ok, complex numbers ok. In so far as linear algebra I am a complete beginner, also anything to do with statistical analysis ie. covariance matrices or state estimation and I'm lost. The Kalman filter algorithm seems to be based on these precepts.
So when I say I'm lost I mean, where do I begin to start with getting to grips with the maths involved. I figure I should work on getting good with linear algebra, should I up my game with calculus as well?
I have seen the Julius Smith stuff before, it is very good, I have covered some of it during some audio dsp courses I have taken, does much of the books here relate directly to Kalman filters?

humbert

I would say that understanding basic probability is most important.

I had to use a Kalman filter about a hear ago to reduce instrument noise in one dimension and it was pretty straight forward. If I can find a link to a particularly useful site explaining it in 1D I'll post it as it helped me get to grips with it a lot.

If I remember correctly (and please correct me if I'm wrong) it suppresses measurements outside the expected variance.

eddyc

I think that is how it works. If you could find that link it would be great.