Both the
estimation and experiment design can be cast as convex optimization
problems. The state estimation follows from the maximum likelihood formulation.
The experiment design procedure is invoked by the
Cramer-Rao Inequality. The resulting optimum design is integer-combinatorial and we use an
established relaxation which results in a convex programming problem
whose solution can be used to guide a more efficient experiment. We
also introduce an adaptive procedure for re-deigning the experiment
and re-estimating the state as new data is recorded. The method is illustrated with both simulated and
experimental photonic data.
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