Fast Kalman Filter
If you have many measurements per update, you should look at the information form of the Kalman filter.  Each additional measurement is just addition.  The tradeoff is a more complex predict step, and the cost of inverting the information matrix whenever you want to get your state out.
I wonder if anyone can give me a pointer to really fast/efficient Kalman filter implementation, possibly in Python (or Cython, but C/C++ could also work if it is much faster). I have a problem with many learning epochs (possibly hundreds of millions), and many input (cues; say, between tens to hundred thousands). Thus, updating a covariance matrix will be a big issue. I read a bit about Ensemble KF, but, for now, I would really like to stick with the standard KF. [ I started reading and testing it, and I would like to give it a try with my real data. ]