Scalable probabilistic gas distribution mapping using Gaussian belief propagation

This paper advocates the Gaussian belief propagation solver for factor graphs in the case of gas distribution mapping to support an olfactory sensing robot. The local message passing of belief propagation moves away from the standard Cholesky decomposition technique, which avoids solving the entire factor graph at once and allows for only areas of interest to be updated more effectively. Implementing a local solver means that iterative updates to the distribution map can be achieved orders of magnitude quicker than conventional direct solvers which scale computationally to the size of the map. After defining the belief propagation algorithm for gas mapping, several state of the art message scheduling algorithms are tested in simulation against the standard Cholesky solver for their ability to converge to the exact solution. Testing shows that under the wildfire scheduling method for a large urban scenario, that distribution maps can be iterated at least 10 times faster whilst still maintaining exact solutions. This move to an efficient local framework allows future works to consider 3D mapping, predictive utility and multi-robot distributed mapping.