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Figure 2 shows two automobiles in a car following model where the objective of the follower vehicle is to maintain a fired distance. For this question, we will assume the

velocity of the vehicles are the same and that the distance between the vehicles is to remain a constant as well. In order to achieve this, the follower vehicle continuously measures the distance between the vehicle in front with the help of a font-bumper mounted radar. Based on the estimated distance, î, the vehicle adjusts its controls to maintain a constant distance. The measurement by the radar can be modelled as z_{i}=x+w_{i} where z, denotes the measurement at time instant i, r denotes the true distance between thevehicles, and w; denotes the measurement noise that is assumed to be zero mean i.i.d. Gaussianwith standard deviation ơ.

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