Reference no: EM131083457
Continuing Problem 11.4.5 of the noisy predictor, generate sample paths of Xn and Yn for n = 0, 1,..., 50 with the following parameters:
(a) c = 0.9, d = 10
(b) c = 0.9, d = 1
(c) c = 0.9, d = 0.1
(d) c = 0.6, d = 10
(e) c = 0.6, d = 1
(f) c = 0.6, d = 0.1
In each experiment, use η = σ = 1. Use the analysis of Problem 11.4.5 to interpret your results.
Problem 11.4.5
Suppose Xn is a random sequence satisfying
Where Z1, Z2,... is an iid random sequence with E[Zn] = 0 and Var[Zn] = σ2 and c is a constant satisfying |c| 0] = 0 and Var[X=] = σ2/(1 - c2). We make the following noisy measurement
Where W1, W2,... is an iid measurement noise sequence with E[Wn] = 0 and Var[Wn] = η2 that is independent of Xn and Zn.
(a) Find the optimal linear predictor, 
n(Yn-1), of Xn using the noisy observation Yn-1.
(b) Find the mean square estimation error
