Find the mean square estimation error

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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

Reference no: EM131083457

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