3. (20pts) Consider the I-state system i= -7W y=x+v where w is plant disturbance and o is sensor noise. They are zero-mean uncorrelated white noise processes with respective variances W = 2 and V = 1. a) (15pts) Derive the Kalman filter gain of this system by solving the ARE SA + AS - SCTV 'CS + W = 0 and noting that the optimal gain is given by K- = SCTV-1, b) (5pts) Write the differential equation of the filter(observer)