QUESTION 1. (10 marks) If the predicted state and uncertainty of a moving agent are $k = 250 39 and the process variance and covariance matrix Pk After At, a sensor measurement is taken which shows that measured state of the moving agent is zk = 257 41 and according to the character- istics of the sensors, the process variance and covariance matrix Rk = [1 2] i. If scalling matrix H = [oi] calculate Kalman gain K. ii. Compute the updated state and uncertainty of the moving object. Hint: We represent: the predicted measurement with (H0, 20) = (H;&k,H_P_H]), and the observed measurement with (41, 1) = (Z*,Rk). The updated state and process covariance matrix are represented as follows: H184 = H2&k+K(2x - Hk) HEPH = HPH -KH PH Where K is: K =H_P_H_(H_P_H+Rx)-1