We will consider the specic case with data 1 8 2 20 1

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Unformatted text preview: lotting (ˆml )i versus yi , with yi on the vertical estimated function φ z axis and (ˆml )i on the horizontal axis.) z Hint. You can assume the measurements are numbered so that yi are sorted in nondecreasing order, i.e., y1 ≤ y2 ≤ · · · ≤ ym . (The data given in the problem instance for part (b) is given in this order.) 6.6 Maximum likelihood estimation of an increasing nonnegative signal. We wish to estimate a scalar signal x(t), for t = 1, 2, . . . , N , which is known to be nonnegative and monotonically nondecreasing: 0 ≤ x(1) ≤ x(2) ≤ · · · ≤ x(N ). This occurs in many practical problems. For example, x(t) might be a measure of wear or deterioration, that can only get worse, or stay the same, as time t increases. We are also given that x(t) = 0 for t ≤ 0. We are given a noise-corrupted moving average of x, given by k y ( t) = τ =1 h(τ )x(t − τ ) + v (t), t = 2, . . . , N + 1, where v (t) are independent N (0, 1) random variables. (a) Show how to formulate the problem of finding the maximum likelihood estimate of...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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