To Örebro University

Gas distribution models can provide comprehensive information about a large number of gas concentration measurements, highlighting, for example, areas of unusual gas accumulation. They can also help to locate gas sources and to plan where future measurements should be carried out. Current physical modeling methods, however, are computationally expensive and not applicable for real world scenarios with real-time and high resolution demands. This chapter reviews kernel methodsthat statistically model gas distribution. Gas measurements are treated as randomvariables, and the gas distribution is predicted at unseen locations either using akernel density estimation or a kernel regression approach. The resulting statistical 

apmodelsdo not make strong assumptions about the functional form of the gas distribution,such as the number or locations of gas sources, for example. The majorfocus of this chapter is on two-dimensional models that provide estimates for themeans and predictive variances of the distribution. Furthermore, three extensionsto the presented kernel density estimation algorithm are described, which allow toinclude wind information, to extend the model to three dimensions, and to reflecttime-dependent changes of the random process that generates the gas distributionmeasurements. All methods are discussed based on experimental validation usingreal sensor data.