Evaluating sensor allocations using equivalence classes of multi-target paths

We present an algorithm for evaluating sensor allocations using simulation of equivalence classes of possible futures. Our method is meant to be used for pre-planning sensor allocations, e.g., for choosing between several alternative flight-paths for UAV´s, or deciding where to deploy ground sensor networks. The method can be used to choose the best sensor allocation with respect to any fusion method. In addition to the list of sensor allocations to evaluate, the algorithm requires knowledge of the terrain/road network of the region of interest. Additional doctrinal knowledge on the enemy´s possible goals and rules of engagement can increase the speed of the method, but is not required. Given a current situation picture, the method generates possible future paths for the objects of interest. For each considered sensor allocation, these futures are partitioned into equivalence classes. Two futures are considered equivalent with respect to a given sensor allocation if they would give rise to the same set of observations. For each such equivalence class, we run a fusion algorithm; in this paper, an emulated multi-target tracker. We use the output of this emulated filter to determine a fitness for each sensor allocation under evaluation. For small scenarios, we compare some different ways of calculating this fitness, concluding that an approximation introduced by us gives nearly the same result as an exact method. We also introduce a formulation of the studied problem and the method used to solve it using random sets, and give several directions for future work.