Suppose we are allowed to observe a random process Z (t) at two points in time, t0 and t2. Based on those observations we would like to estimate Z (t) at time t = t1 where t0 < t1 < t2. We can view this as an interpolation problem. Let our estimator be a linear combination of the two observations,
Y (t1) = Ẑ (t1) = aZ (t0) + bZ (t2)
(a) Use the orthogonality principle to find the MMSE estimator.
(b) Find an expression for the mean square error of the MMSE estimator.