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This paper provides conditions on the observation probability distribution inBayesian localization and optimal filtering so that the conditional meanestimate satisfies convex stochastic dominance. Convex dominance allows us tocompare the unconditional mean square error between two optimal Bayesian stateestimators over arbitrary time horizons instead of using brute forceMonte-Carlo computations. The proof uses two key ideas from microeconomics,namely, integral precision dominance and aggregation of single crossing.Theconvex dominance result is then used to give sufficient conditions so that theoptimal policy of a controlled sensing two-state partially observed Markovdecision process (POMDP) is lower bounded by a myopic policy. Numericalexamples are presented where the Shannon capacity of the observationdistribution using one sensor dominates that of another, and convex dominanceholds but Blackwell dominance does not hold. These illustrate the usefulness ofthe main result in localization, filtering and controlled sensing applications.

Convex Stochastic Dominance in Bayesian Localization, Filtering and Controlled Sensing POMDPs