Inverse problems in atmospheric dispersion with randomly scattered sensors

We consider the problem of monitoring the concentration and dispersion of pollutants in the atmosphere using a collection of randomly scattered sensors. The sensors are capable of only indicating that the concentration has exceeded a randomly selected threshold and providing this information through a transponder-like mechanism to an airborne imaging radar. We use this information together with a standard atmospheric dispersion model to estimate the concentration as well as the time and location of the pollutant source. We use the expectation–maximization algorithm to find the maximum likelihood estimate of the quantities of interest.