$(10$ points$)$: Observer $($State Estimator$)$ and Kalman Filter $1.$ Assume that we have developed a state$-$space model of our physical system $=+([+1]=$

$[]+[])$ In a few sentences, give $2-3$ reasons why we may want to use an observer for our physical system we are trying to control.

$2.$ What information is used in the observer $($state estimator$)$ that might enable us to get better estimates of the

actual states of the physical system when compared to performing a forward simulation.

$3.$ What is a defining feature of a Kalman Filter that makes it different from a deterministic $($Luenberger$)$ observer.

What additional information is included in a Kalman Filter?