Why is the Kalman filter a filter and not a control system? The Kalman filter is a recursive filter which can be used to estimate the internal state of a linear dynamic system with noise in the signal(s). Isn't that the same as a traditional feedforward/feedback control structure (figure below)? The feedforward controller modification uses anticipated results in the form of a mathematical model, predicting. Then the feedback controller would update the state and give feedback, updating.
A Kalman Filter (estimator is actually more apt than filter) simply estimates states, that's all it does. It, by itself, cannot drive a plant towards a desired output. The estimated states are used to determine how far off the plant is from the desired state. Controls are implemented after KF has already been used to obtain the current state.
Referring to the block diagram, the KF block will be placed in the feedback path from the output $y$. Assuming the plant's output is observed by at least one sensor, the KF uses the plant's own model (prediction update) along with the sensor readings (measurement update) to estimate the current state of the plant. All sensors are noisy and the plant's model will not be perfect, so how good the estimates are will be determined by how well sensor noise and the plant has been modeled.
The state estimate produced by the KF is compared with the setpoint $r$ to obtain the error. Up until this point, no control action has taken place, the plant's current state has merely been observed. The control kicks in after you've determined the error. So the Kalman Filter is not really a control system.