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Unformatted text preview: lving this problem, using convex optimization.
(There are many diﬀerent approaches which work quite well.)
You might ﬁnd the following fact useful. The solution to
minimize Ax − P T y over P ∈ Rm×m a permutation matrix, is the permutation that matches the smallest entry in y
with the smallest entry in Ax, does the same for the second smallest entries and so forth.
Carry out your method on the data in ls_perm_meas_data.m. Give your estimate of the permuted
indices. The data ﬁle includes the true permutation matrix and value of x (which of course you
cannot use in forming your estimate). Compare the estimate of x you get after your guessed
permutation with the estimate obtained assuming P = I .
Remark. This problem comes up in several applications. In target tracking, we get multiple noisy
measurements of a set of targets, and then guess which targets are the same in the diﬀerent sets of
measurements. If some of our guesses are wrong (i.e., our target association is wrong) we have the
present problem. In vision...
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