Resource allocation for signal detection with active sensors

We consider the problem of determining the existence of known constant signals over a set of sites, given noisy measurements obtained by a team of active sensors that can switch between different sites. Since the quality of detection depends on the time that the sensors allocate at every site, maximizing the total detection probability relies on selecting the sites and possibly the order in which these should be monitored. When the switching time between sites is negligible, as in steerable camera networks, we show that optimizing the global detection performance for a team of sensors with uncorrelated measurement noise is a convex problem. On the other hand, for significant switching times, which can be due to path planning for mobile robots in surveillance missions, the detection problem can be approximated by an integer program, known as the orienteering problem. Due to its hardness, even small instances of this problem are difficult to solve. Focusing on the single sensor problem, we propose a heuristic that employs the well studied traveling salesman problem to determine an optimal sequence of sites that maximizes the available time for detection. We finally show that when the switching penalties can be captured by a constraint on the number of sites to be observed, then submodularity of the unconstrained performance objective results in an effective greedy algorithm for selecting these sites.