Find the optimal linear predictor

Reference no: EM131083341

Suppose X_n 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[W_n] = 0 and Var[W_n] = η² that is independent of X_n and Z_n.

(a) Find the optimal linear predictor, _n(Y_n-1), of X_n using the noisy observation Y_n-1.

(b) Find the mean square estimation error

Reference no: EM131083341

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