Bayesian spatial event distribution grid maps for modeling the spatial distribution of gas detection events

In this paper we introduce a novel gas distribution mapping algorithm, Bayesian Spatial Event Distribution (BASED), that, instead of modeling the spatial distribution of a quasi-continuous gas concentration, models the spatial distribution of gas events, for example detection and non-detection of a target gas. The proposed algorithm is based on the Bayesian Inference framework and models the likelihood of events at a certain location with a Bernoulli distribution. In order to avoid overfitting, a Bayesian approach is used with a beta distribution prior for the parameter μ that governs the Bernoulli distribution. In this way, the posterior distribution maintains the same form of the prior, i.e., will be a beta distribution as well, enabling a simple approach for sequential learning. To learn a map composed of beta distributions, we discretize the inspection area into a grid and extrapolate from local measurements using Gaussian kernels. We demonstrate the proposed algorithm for MOX sensors and a photo ionization detector mounted on a mobile robot and show how qualitatively similar maps are obtained from very different gas sensors.