Abstract: In a sparse sensor array for detecting the progression of a cloud of gas within a confined space, a method is disclosed for estimating a distribution of the cloud of gas throughout the confined space. The method includes determining at each interval a plurality of functions representing possible distributions of the gas cloud by a Gaussian process, employing a particle filtering process to predict the progression of each such function at a subsequent sampling instant, using a diffusion equation for the gas cloud, attaching a likelihood value to each function at the subsequent sampling instant, and determining a revised set of functions with associated likelihood values, and repeating the above steps.