Stochastic Control Bounds on Sensor Network Performance

Consider a network of sensors, each of which has limited sensing resources, which is tasked with collecting noisy classification information on objects. The amount of resources required a given sensor to measure an object depends on the specific sensor-object geometry. Sensors exchange collected information to estimate object identities and coordinate which measurements to collect. This paper describes a computable lower bound on the classification error that can be achieved by a causal adaptive sensing schedule. This bound is based on solving a partially observed stochastic control problem. Expanding the admissible control space of this problem leads to a relaxed problem with simpler decision structure for which the bounds can be computed. The bound computations are illustrated for examples involving 100 unknown objects, and compared with the Monte Carlo performance of specific scheduling algorithms. These comparisons illustrate the tightness of the bounds.