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Unformatted text preview: de. Is X
convex?
Now we will examine what happens when the measurements are occasionally in error, i.e., for a few
i we have no relation between x and yi . More precisely suppose that Ifault is a subset of {1, . . . , K },
and that yi = Ax + vi with vi ∞ ≤ α (as above) for i ∈ Ifault , but for i ∈ Ifault , there is no relation
between x and yi . The set Ifault is the set of times of the faulty measurements.
Suppose you know that Ifault has at most J elements, i.e., out of K measurements, at most J are
faulty. You do not know Ifault ; you know only a bound on its cardinality (size). For what values of
J is X , the set of x consistent with the measurements, convex?
5.12 Leastsquares with some permuted measurements. We want to estimate a vector x ∈ Rn , given
some linear measurements of x corrupted with Gaussian noise. Here’s the catch: some of the
measurements have been permuted.
More precisely, our measurement vector y ∈ Rm has the form
y = P (Ax + v ),
47 where vi are IID N (0, 1) measurement noises, x ∈ Rn is the vector...
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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 University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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