Table of Contents Author Guidelines Submit a Manuscript
Mobile Information Systems
Volume 2016, Article ID 9595306, 15 pages
http://dx.doi.org/10.1155/2016/9595306
Research Article

Measuring the Uncertainty of Probabilistic Maps Representing Human Motion for Indoor Navigation

German Aerospace Center (DLR), Institute for Communications and Navigation, Oberpfaffenhofen, Germany

Received 17 February 2016; Accepted 7 August 2016

Academic Editor: Yuwei Chen

Copyright © 2016 Susanna Kaiser et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Seco-Granados, J. A. López-Salcedo, D. Jiménez-Baños, and G. López-Risueno, “Challenges in indoor global navigation satellite systems: unveiling its core features in signal processing,” IEEE Signal Processing Magazine, vol. 29, no. 2, pp. 108–131, 2012. View at Publisher · View at Google Scholar · View at Scopus
  2. H. Liu, H. Darabi, P. Banerjee, and J. Liu, “Survey of wireless indoor positioning techniques and systems,” IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews, vol. 37, no. 6, pp. 1067–1080, 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. R. Mautz, Indoor positioning technologies [Habilitation thesis], ETH Zürich, Zürich, Switzerland, 2012.
  4. E. Foxlin, “Pedestrian tracking with shoe-mounted inertial sensors,” IEEE Computer Graphics and Applications, vol. 25, no. 6, pp. 38–46, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. R. Harle, “A survey of indoor inertial positioning systems for pedestrians,” IEEE Communications Surveys & Tutorials, vol. 15, no. 3, pp. 1281–1293, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Beauregard, W. Widyawan, and M. Klepal, “Indoor PDR performance enhancement using minimal map information and particle filters,” in Proceedings of the IEEE/ION Position, Location and Navigation Symposium (PLANS '08), pp. 141–147, IEEE, Monterey, Calif, USA, May 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. B. Krach and P. Roberston, “Cascaded estimation architecture for integration of foot-mounted inertial sensors,” in Proceedings of the IEEE/ION Position, Location and Navigation Symposium (PLANS '08), pp. 112–119, IEEE, Monterey, Calif, USA, May 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. O. Woodman and R. Harle, “Pedestrian localisation for indoor environments,” in Proceedings of the 10th International Conference on Ubiquitous Computing (UbiComp '08), pp. 114–123, Seoul, South Korea, September 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. H. Durrant-Whyte and T. Bailey, “Simultaneous localization and mapping: part I,” IEEE Robotics & Automation Magazine, vol. 13, no. 2, pp. 99–110, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Smith, M. Self, and P. Cheeseman, “Estimating uncertain spatial relationships in robotics,” in Autonomous Robot Vehicles, I. Cox and E. G. T. Wilfon, Eds., pp. 167–193, Springer-Verlag, New York, 1990. View at Google Scholar
  11. P. Robertson, M. Angermann, and B. Krach, “Simultaneous localization and mapping for pedestrians using only foot-mounted intertial sensors,” in Proceedings of the 11th International Conference on Ubiquitous Computing (UbiComp '09), pp. 93–96, ACM, Orlando, Fla, USA, 2009. View at Publisher · View at Google Scholar
  12. A. Doucet, N. De Freitas, K. Murphy, and S. Russell, “Rao-Blackwellised particle filtering for dynamic Bayesian networks,” in Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence (UAI '00), pp. 176–183, Morgan Kaufmann Publishers Inc, Stanford, Calif, USA, June 2000.
  13. M. Montemerlo, S. Thrun, D. Koller, and B. Wegbreit, “FastSLAM: a factored solution to the simultaneous localization and mapping problem,” in Proceedings of the AAAI National Conference on Artificial Intelligence, Edmonton, Canada, 2002.
  14. S. Kaiser and E. Munoz Diaz, “PocketSLAM based on the principle of the FootSLAM algorithm,” in Proceedings of the International Conference on Localization and GNSS (ICL-GNSS '15), pp. 1–5, Götheburg, Sweden, June 2015. View at Publisher · View at Google Scholar
  15. S. Julier and J. Uhlmann, “A new extension of the Kalman filter to nonlinear systems,” in Proceedings of the 11th International Symposium on Aerospace on Aerospace/Defence Sensing, Simulation and Controls (AeroSense '97), Orlando, Fla, USA, April 1997.
  16. E. Wan and R. Van Der Merwe, “The unscented Kalman filter for nonlinear estimation,” in Proceedings of the IEEE Adaptive Systems for Signal Processing, Communications, and Control Symposium (AS-SPCC '00), pp. 153–158, IEEE, Lake Louise, Canada, 2000.
  17. F. Zampella, M. Khider, P. Robertson, and A. Jiménez, “Unscented Kalman filter and Magnetic Angular Rate Update (MARU) for an improved Pedestrian Dead-Reckoning,” in Proceedings of the IEEE/ION Position Location and Navigation Symposium (PLANS '12), pp. 129–139, IEEE, Myrtle Beach, SC, USA, April 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Transactions on Signal Processing, vol. 50, no. 2, pp. 174–188, 2002. View at Publisher · View at Google Scholar · View at Scopus
  19. P. Robertson, M. Garcia Puyol, and M. Angermann, “Collaborative pedestrian mapping of buildings using inertial sensors and FootSLAM,” in Proceedings of the 24th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS '11), pp. 1366–1377, Portland, Ore, USA, 2011.
  20. T. M. Cover and J. A. Thomas, Elements of Information Theory, John Wiley & Sons, 2nd edition, 2006. View at MathSciNet
  21. M. Angermann and P. Robertson, “FootSLAM: pedestrian simultaneous localization and mapping without exteroceptive sensors—hitchhiking on human perception and cognition,” Proceedings of the IEEE, vol. 100, pp. 1840–1848, 2012. View at Publisher · View at Google Scholar · View at Scopus
  22. J. T. Bjørke, “Framework for entropy-based map evaluation,” Cartography and Geographic Information Systems, vol. 23, no. 2, pp. 78–95, 1996. View at Publisher · View at Google Scholar · View at Scopus
  23. G. J. Klir and T. A. Folger, Fuzzy Sets, Uncertainty, and Information, Prentice Hall, New York, NY, USA, 1988. View at MathSciNet
  24. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication, The University of Illinois Pressl, Urbana, Ill, USA, 1964.
  25. D. Guo, “Local entropy map: a nonparametric approach to detecting spatially varying multivariate relationships,” International Journal of Geographical Information Science, vol. 24, no. 9, pp. 1367–1389, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. A. Rényi, “On measures of information and entropy,” in Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, pp. 547–561, Menlo Park, Calif, USA, 1960.
  27. C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal, vol. 27, no. 3, pp. 379–423, 1948. View at Publisher · View at Google Scholar · View at MathSciNet
  28. T. Arbel and F. P. Ferrie, “Entropy-based gaze planning,” Image and Vision Computing, vol. 19, no. 11, pp. 779–786, 2001. View at Publisher · View at Google Scholar · View at Scopus
  29. J. L. Blanco, J. A. Fernndez-Madrigal, and J. Gonzalez, “A novel measure of uncertainty for mobile robot SLAM with rao-blackwellized particle filters,” International Journal of Robotics Research, vol. 27, no. 1, pp. 73–89, 2008. View at Publisher · View at Google Scholar · View at Scopus
  30. C. Stachniss, G. Grisetti, and W. Burgard, “Information gain-based exploration using rao-blackwellized particle filters,” in Proceedings of the Robotics: Science and Systems (RSS '05), Cambridge, Mass, USA, 2005.
  31. C. Song, Z. Qu, N. Blumm, and A.-L. Barabási, “Limits of predictability in human mobility,” Science, vol. 327, no. 5968, pp. 1018–1021, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. G. Smith, R. Wieser, and J. Goulding, “A refined limit on the predictability of human mobility,” in Proceedings of the IEEE International Conference on Pervasive Computing and Communications (PERCOM '14), Orlando, Fla, USA, March 2014.
  33. R. H. Berg, Wargame Design: The History, Production, and Use of Conflict Simulation Games (Strategy & Tactics Staff Study), Hippocrene Books, Madison, Wis, USA, 1st edition, 1981.
  34. P. Doyle and J. L. Snell, Random Walks and Electric Networks, Mathematical Association of America, 1984.
  35. L. Lovász, “Random walks on graphs: a survey,” Combinatorics, Paul Erdös Is Eighty, vol. 2, pp. 1–46, 1993. View at Google Scholar
  36. D. Heckerman, “A tutorial on learning with Bayesian networks,” Tech. Rep., Microsoft Research, Redmond, Washington, DC, USA, 1995. View at Google Scholar
  37. E. L. W. David and A. L. Y. Peres, Markov Chains and Mixing Times, American Mathematical Society, Providence, RI, USA, 1st edition, 2008.
  38. Z. Rached, F. Alajaji, and L. L. Campbell, “The Kullback-Leibler divergence rate between Markov sources,” IEEE Transactions on Information Theory, vol. 50, no. 5, pp. 917–921, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. M. Anisi and M. Analoui, “Multinomial agent's trust modeling using entropy of the Dirichlet distribution,” International Journal of Artificial Intelligence & Applications, vol. 2, no. 3, pp. 1–11, 2011. View at Publisher · View at Google Scholar
  40. W. Penny, KL-Divergences of Normal, Gamma, Dirichlet, and Wishart Densities, 2001, http://www.fil.ion.ucl.ac.uk/~wpenny/publications/densities.ps.