Achim J. Lilienthal, Matteo Reggente, Marco Trincavelli, Jose Luis Blanco, and Javier Gonzalez
A Statistical Approach to Gas Distribution Modelling with Mobile Robots The Kernel DM+V Algorithm
Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS), 2009, pp. 570-576
Abstract: Gas distribution modelling constitutes an ideal application area for mobile robots, which as intelligent mobile gas sensors offer several advantages compared to stationary sensor networks. In this paper we propose the Kernel DM+V algorithm to learn a statistical 2-d gas distribution model from a sequence of localized gas sensor measurements. The algorithm does not make strong assumptions about the sensing locations and can thus be applied on a mobile robot that is not primarily used for gas distribution monitoring, and also in the case of stationary measurements. Kernel DM+V treats distribution modelling as a density estimation problem. In contrast to most previous approaches, it models the variance in addition to the distribution mean. Estimating the predictive variance entails a significant improvement for gas distribution modelling since it allows to evaluate the model quality in terms of the data likelihood. This offers a solution to the problem of ground truth evaluation, which has always been a critical issue for gas distribution modelling. Estimating the predictive variance also provides the means to learn meta parameters and to suggest new measurement locations based on the current model. We derive the Kernel DM+V algorithm and present a method for learning the hyper-parameters. Based on real world data collected with a mobile robot we demonstrate the consistency of the obtained maps and present a quantitative comparison, in terms of the data likelihood of unseen samples, with an alternative approach that estimates the predictive variance.
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  AUTHOR = {Lilienthal, Achim~J. and Reggente, Matteo and Trincavelli, Marco and Blanco, Jose Luis and Gonzalez, Javier},
  TITLE = {A Statistical Approach to Gas Distribution Modelling with Mobile Robots The Kernel DM+V Algorithm},
  BOOKTITLE = {Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
  YEAR = {2009},
  MONTH = {October 11 -- October 15},
  ADRESS = {St. Louis, USA},
  PAGES = {570-576}