# Why assume controls are independent of state estimation in Kalman Filter?

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

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:

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

• If the control is $\{u_i\}$ then those are controlled by a person. They aren't random. Nov 8, 2017 at 22:38
• 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). Nov 10, 2017 at 2:18
• you could. If it isn't random, it isn't random. Nov 10, 2017 at 2:29
• 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. Nov 10, 2017 at 21:44