The Entropy of Cooperative Radiation Sensing by Distributed Sensors

By expressing the expected collective radiation counts registered by the robotic swarm, at any given workspace location as a function of the prior knowledge about the distribution of radiation intensity in the workspace, the sensor geometry, and the sensors’ trajectories, we apply Bayes’ rule to obtain the probability density function of local radiation intensity conditioned on the collected measurements and the trajectory of the sensor. From this, we derive analytical expressions for the entropy of the distributed sensing system as a function of time. We show that the entropy of the distributed sensing system is stable and converges to steady state values.