Sensor Placement for A Pairwise Sensing Model: Framework and Algorithms

In this paper, we discuss the problem of placing the minimum number of sensors in a given area such that all points in that area are covered by the sensors. We consider a pairwise sensing model where each pair of sensors has an associated sensing area. This model arises in applications like structural health monitoring where a transducer network monitors a structure by exciting one transducer at a time while other transducers collect the data. We first formulate the placement as an optimization problem using a grid-based approach. We present a greedy algorithm to solve the optimization problem. We also present a faster version of the greedy algorithm based on column elimination and recursive updates. To further improve the greedy method, we use a group-greedy strategy. This strategy is a compromise between the conventional greedy method and an exhaustive search. Finally, we apply our algorithm to the structural health monitoring application. Using numerical results, we demonstrate the efficacy of our algorithm and show that the solution is close to the optimal solution.