A collection of static and mobile radiation sensors is tasked with deciding, within a fixed time interval, whether a moving target carries radioactive material. Formally, this is a problem of detecting weak time-inhomogeneous Poisson signals (target radiation) concealed in another Poisson signal (naturally occurring background radiation). Each sensor locally processes its observations to form a likelihood ratio, which is transmitted once at the end of the decision interval to a fusion center. The latter combines the transmitted information to optimally (in the Neyman-Pearson sense) decide whether the measurements contain a radiation signal, or just noise. We provide a set of analytically derived upper bounds for the probabilities of false alarm and missed detection, which are used to design threshold tests without the need for computationally intensive Monte Carlo simulations. These analytical bounds couple the physical quantities of interest to facilitate planning the motion of the mobile sensors for minimizing the probability of missed detection. The network reconfigures itself in response to the target motion, to allow more accurate collective decisions within the given time interval. The approach is illustrated in numerical simulations, and its effectiveness demonstrated in experiments that emulate the statistics of nuclear emissions using a pulsed laser. (C) 2014 Elsevier Ltd. All rights reserved.