Efficient Targeting of Sensor Networks for Large-Scale Systems

This paper proposes an efficient approach to an observation targeting problem that is complicated by a combinatorial number of targeting choices and the large dimension of the system state, when the goal is to minimize the uncertainty in some quantities of interest. The primary improvements in the efficiency are obtained by computing the impact of each possible measurement choice on the uncertainty reduction backwards. This backward method provides an equivalent solution to a traditional forward approach under some standard assumptions, while removing the requirement of calculating a combinatorial number of covariance updates. A key contribution of this paper is to prove that the backward approach operates never slower than the forward approach, and that it works significantly faster than the forward one for ensemble-based representations. The primary benefits are shown on a simplified weather problem using the Lorenz-95 model.