(2) Consider the random walk model Xn that satisfies Xn -Xn-1 Zn for n > 0, where is not observable directly but Xo = 0 and Zn is WN(0,1). Suppose that the process only with additive noise, witho is WN(0, 2), independent of Zn. (a) Give the Kalman filter process satisfying Yn-X s for best linear predictor of Xn and its MSE based on the observed process Ym up to time n-1, in other words for all m with m Sn-1 (b) Find the limit as n ? oo of the MSE and use it to give the steady-state Kalman filter equation for best linear predictor

(2) Consider the random walk model Xn that satises X\" = Xn_1 + Zn for n > 0, where X0 = 0 and Zn is WN(0, 1). Suppose that the process X" is not observable directly but only with additive noise, with observation process Iatisfying Yn = Xn + W\