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What would be the prerequisites needed to implement a kalman filter (and of course, understand it)?
I'm currently on my fifth year on engineering in Brazil, and I know:
If possible please cite a starting point for studying the subject as well (books, website).
If you just want to implement Kalman Filtering, and by this mean 'coding it up' and already have the coding skills, nothing really other than a good reference book. Personally, I learned Kalman Filtering from Hamilton, Time Series Analysis; and from Oksendahl, Stochastic Differential Equations; and this gives an idea which direction to look to get a better, true understanding of the Filter. Most importantly, learning some probability theory would certainly help as it's usually cast in that framework. It doesn't have to be measure-theoretic, although it certainly helps if you understand probability on that level. Some probability books I liked and learned from were Williams, Probability with Martingales (also does some filtering), and Ross, Stochastic Processes.
It all depends on how deeply you want to get into it. Don't forget that learning by doing is often the best medicine (and one that I tend to forget): so just grab a reference, code up what you want to use it for, and play with it. Gl! (P.S.: None of the books I mentioned is specifically focused on KF. There are certainly books for that too, but I lack familiarity).
Grewal M.S. & Andrews, A.P. (2001), Kalman Filtering: Theory and Practice, 2nd ed., John Wiley and Sons.
This textbook is an absolute staple, especially for engineers. It serves as a great introduction and a solid reference too. I would highly recommend this, the mathematical prerequisites are fairly limited and given your experience I don't think it'll be too challenging.
The Kalman filter results can be reached through a number of different proofs and this book avoids using any complicated Bayesian analysis, if you're already familiar with the state-space form it's all rather intuitive.
