1) Derive the Kalman filter equations. The main ideas are already given in the handout. You need to write out the details, basically how do you go from the updated state at i-1 to the updated state at i. Need to obtain the prediction step (simple if you remember conditional expectations) and the update step (here need to write out the formula for conditional Gaussians, available in any book, and show how it is applied).
2) Use the guideline given in the handout to derive the Extended Kalman filter equations. Need to first write out correctly the first order Taylor series approximation and then use exactly the same procedure as in obtaining the Kalman filter.