Use the orthogonality principle to find the mmse estimator

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Reference no: EM131218977

Suppose we are allowed to observe a random process Z(r) at two points in time, ro and ri .

Based on those observations we would like to estimate Z(t) at time t = t₂ where t₀ ₁ 2 . We can view this as a prediction problem. Let our estimator be a linear combination of the two observations,

(a) Use the orthogonality principle to find the MMSE estimator.

(b) Suppose that for positive constants b and c. Show that in this case, the sample at time t = to is not useful for predicting the value of the process at time t = t₂ (given we have observed the process at time t = t₁ > t_o ). In other words, show that a = 0 .

Reference no: EM131218977

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