Exploring the Math of Kalman Filters: A College Calculus Student's Guide

[uglyoldbob]

I have been doing some reading on Kalman filters trying to figure where to start. I have done some college level calculus, but clearly I don't currently know enough to understand the math involved. Where is a good place for me to start? I downloaded a copy of the linear algebra book by Jim Hefferon. I haven't read a whole lot of the book, but I feel pretty confident with the topics covered in it.

 

[John Creighto]

Between linear algebra and Calculus that should be enough to understand the Kalman filter.

 

[uglyoldbob]

Every place explaining the kalman filter seems to use completely different variable names which makes it difficult for me to understand.
You have the measured state and the actual state. Then there is a state transition model, a control input model, process noise, and observation noise.
Measured state and actual state are easy. What do those others mean? Are there "standard" variable names for these?
Anybody know where I can find some good explanations for the kalman filter?

 

[D H]

Between linear algebra and Calculus that should be enough to understand the Kalman filter.

I strongly disagree. Without a good understanding of probability and statistics the linear algebra and calculus will just look like a bunch of stuff pulled out of thin air.

Anybody know where I can find some good explanations for the kalman filter?

Here's a free one, "An Introduction to the Kalman Filter," by Welch and Bishop.
http://www.cs.unc.edu/~tracker/media/pdf/SIGGRAPH2001_CoursePack_08.pdf

The book "Introduction to Random Signals and Applied Kalman Filtering" by Brown and Hwang isn't free, but is very very good.
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471128392.html

Both delve extensively into probability and statistics before introducing the filtering concepts.