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Here's the classic graphical model depiction of a Kalman Filter (or any form of Bayes filter for that matter).

enter image description here

Why do we assume that the controls are independent of the previous state estimation? For example, if we are trying to maintain a car's cruise control at 100 km/h, then clearly the control is not independent of the state. In fact, we would often decide on our control with a PID controller for example. So in my mind, it should look somewhat like this:

enter image description here

Is the reason why its not simply mathematical simplification, or is there something deeper I'm not seeing?

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  • $\begingroup$ If the control is $\{u_i\}$ then those are controlled by a person. They aren't random. $\endgroup$
    – Taylor
    Nov 8, 2017 at 22:38
  • $\begingroup$ Not sure if you are agreeing with me or adding to my point? Whether the controls come from a person or from a PID is the same, they are still dependent on the previous state (for example, if you are in front of a wall, you wouldn't give a forward control). $\endgroup$
    – samlaf
    Nov 10, 2017 at 2:18
  • $\begingroup$ you could. If it isn't random, it isn't random. $\endgroup$
    – Taylor
    Nov 10, 2017 at 2:29
  • $\begingroup$ I know you could. I was wondering whether it makes the mathematics much more difficult in some places, which would explain why its not usually done this way. $\endgroup$
    – samlaf
    Nov 10, 2017 at 21:44

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