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These equations predict what the current state is based from the last state and the commanded action.

To validate my own scattered knowledge of this subject I need to ask for a clarification. I'm not trying to be a nitpicking prick, so please don't take it that way. I'm just trying to get it down in my own mind. Is this a more accurate statement? "These equations predict what the current state is based from the last state and the last commanded action."

what if you have a PID (or PI or PD or P or whatever) control of say a velocity and you update at 50 hz, and you are going to run your Kalman Filter at 10 hz. I'm guessing you include the error of the PID into Q, and then buffer the last command into the PID u action along with steering commands if you are talking Ackermann model?

You by chance wouldn't be able to recommend a good book that covers Kalman Filters, and other control theory kind of stuff. I just had my yearly review and they said they would kick in for some high quality books, so I'm just kinda hunting around at the moment.

Here is some c code for a kalman filter I designed for a PUMA 3DOF robotic arm ....

I think this is c++.