A Kalman filter based approach to probabilistic gas distribution mapping

Building a model of gas concentrations has important industrial and environmental applications, and mobile robots on their own or in cooperation with stationary sensors play an important role in this task. Since an exact analytical description of turbulent flow remains an intractable problem, we propose an approximate approach which not only estimates the concentrations but also their variances for each location. Our point of view is that of sequential Bayesian estimation given a lattice of 2D cells treated as hidden variables. We first discuss how a simple Kalman filter provides a solution to the estimation problem. To overcome the quadratic computational complexity with the mapped area exhibited by a straighforward application of Kalman filtering, we introduce a sparse implementation which runs in constant time. Experimental results for a real robot validate the proposed method.