  This paper addresses active state estimation with a team of robotic sensors.
The states to be estimated are represented by spatially distributed,
uncorrelated, stationary vectors. Given a prior belief on the geographic
locations of the states, we cluster the states in moderately sized groups and
propose a new hierarchical Dynamic Programming (DP) framework to compute
optimal sensing policies for each cluster that mitigates the computational cost
of planning optimal policies in the combined belief space. Then, we develop a
decentralized assignment algorithm that dynamically allocates clusters to
robots based on the pre-computed optimal policies at each cluster. The
integrated distributed state estimation framework is optimal at the cluster
level but also scales very well to large numbers of states and robot sensors.
We demonstrate efficiency of the proposed method in both simulations and
real-world experiments using stereoscopic vision sensors.
