  Unresolved data association in ambiguous and perceptually aliased
environments leads to multi-modal hypotheses on both the robot's and the
environment state. To avoid catastrophic results, when operating in such
ambiguous environments, it is crucial to reason about data association within
Belief Space Planning (BSP). However, explicitly considering all possible data
associations, the number of hypotheses grows exponentially with the planning
horizon and determining the optimal action sequence quickly becomes
intractable. Moreover, with hard budget constraints where some non-negligible
hypotheses must be pruned, achieving performance guarantees is crucial. In this
work we present a computationally efficient novel approach that utilizes only a
distilled subset of hypotheses to solve BSP problems while reasoning about data
association. Furthermore, to provide performance guarantees, we derive error
bounds with respect to the optimal solution. We then demonstrate our approach
in an extremely aliased environment, where we manage to significantly reduce
computation time without compromising on the quality of the solution.
