Fast Kalman Filter
The size of the covariance matrix is driven by the size of your state. Another question relates to the assumptions on your model and if this can bring up significant optimizations (obviously, optimizing implies reworking the "standard KF"). 
From my POV, your situation roughly depends on the value (number_of_states² * number_of_iterations)/(processing_power).
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. ]