We are asked to estimate the displacement of large vehicles (semi-trailers) when parked on the shoulder of a freeway and subjected to wind gusts created by passing vehicles. We measure the...

We are asked to estimate the displacement of large vehicles (semi-trailers)

when parked on the shoulder of a freeway and subjected to wind gusts created by passing vehicles. We measure the displacement of the vehicle by placing an accelerometer on the trailer. The accelerometer has inherent inaccuracies which is modeled as

y = K_ax + n

with y, x, and n, the measured and actual displacement and white measurement noise of variance, Rnn and Ka the instrument gain. The dynamics of the vehicle can be modeled by a simple mass-spring-damper.

(a) Construct and identify the measurement model of this system.

(b) Construct and identify the process model and model-based estimator for this problem.