Problem 2. As in the Kalman filtering Theorem 3.4.1, consider the state space system x(n + 1) = Ax(n) + Bu(n) and y(n) = Cx(n) + Du(n) (3.16) where u(n) and v(n) are independent white noise random processes, which are independent to the initial condition x(0). Recall that Mn equals the linear span of {y(k) } , and the optimal state estimate in the Kalman filter is given by a(n) = PMn_ x(). Find the state estimate PM,x(n) for x(n) in terms of x(n) and y(n). Hint, according to Lemma 3.3.1, we have PMnf = PMn-If + Rip(n) R(n) 4(n), (3.17) where f is any random vector, and p(n) = y(n) - PMn-14(n)