Q.10) Delayed Kalman Filter:

Consider a process with the transition rule xn+1 = axn + vn where vn N (0, 2 v ). We can only observe the process at even-numbered times, i.e. we see y2n = x2n + w2n, where wn N (0, 2 w).

1. Find a recurrence relation for the MMSE of the even states x2n = E[x2n|y0, y2, . . . , y2n] in terms of x2n2.

2. Find a recurrence relation for the MMSE of the odd states x2n+1 = E[x2n+1|y0, y2, . . . , y2n] in terms of x2n.