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Abstract

The trace of a moving object is commonly referred to as a trajectory. This paper considers the spatio-temporal information content of a discrete trajectory in relation to a movement prediction model for the object under consideration. The information content is the minimal amount of information necessary to reconstruct the trajectory, given the movement model. We show how the information content of arbitrary trajectories can be determined and use these findings to derive an approximative arithmetic coding scheme for trajectory information, reaching a level of compression that is close to the bound provided by its entropy. We then demonstrate the practical applicability of our ideas by using them to compress real-world vehicular trajectories, showing that this vastly improves upon the results provided by the best existing schemes.

Keywords

Information Content Compression Ratio Movement Estimation Movement Model Compression Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Lange, R., Farrell, T., Dürr, F., Rothermel, K.: Remote real-time trajectory simplification. In: PerCom 2009: Proceedings of the 7th IEEE International Conference on Pervasive Computing and Communications, pp. 184–193 (March 2009)Google Scholar
  2. 2.
    Hönle, N., Großmann, M., Reimann, S., Mitschang, B.: Usability analysis of compression algorithms for position data streams. In: GIS 2010: Proceedings of the 18th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (November 2010)Google Scholar
  3. 3.
    Ni, J., Ravishankar, C.V.: Indexing Spatio-Temporal Trajectories with Efficient Polynomial Approximations. IEEE Transactions on Knowledge and Data Engineering 19, 663–678 (2007)CrossRefGoogle Scholar
  4. 4.
    Koegel, M., Kiess, W., Kerper, M., Mauve, M.: Compact Vehicular Trajectory Encoding. In: VTC 2011-Spring: Proceedings of the 73rd IEEE Vehicular Technology Conference (May 2011)Google Scholar
  5. 5.
    Civilis, A., Jensen, C.S., Pakalnis, S.: Techniques for efficient road-network-based tracking of moving objects. IEEE Transactions on Knowledge and Data Engineering 17(5), 698–712 (2005)CrossRefGoogle Scholar
  6. 6.
    Cao, H., Wolfson, O., Trajcevski, G.: Spatio-temporal data reduction with deterministic error bounds. VLDB Journal 15(3), 211–228 (2006)CrossRefGoogle Scholar
  7. 7.
    Imai, H., Iri, M.: Computational-geometric methods for polygonal approximations of a curve. Computer Vision, Graphics, and Image Processing 36(1), 31–41 (1986)CrossRefGoogle Scholar
  8. 8.
    Baran, I., Lehtinen, J., Popovic, J.: Sketching Clothoid Splines Using Shortest Paths. In: Computer Graphics Forum, pp. 655–664 (2010)Google Scholar
  9. 9.
    Koegel, M., Baselt, D., Mauve, M., Scheuermann, B.: A Comparison of Vehicular Trajectory Encoding Techniques. In: MedHocNet 2011: Proceedings of the 10th Annual Mediterranean Ad Hoc Networking Workshop (June 2011)Google Scholar
  10. 10.
    Fox, D.: Markov localization: A probabilistic framework for mobile robot localization and navigation. Ph.D. dissertation, University of Bonn, Germany (1998)Google Scholar
  11. 11.
    Roy, N., Burgard, W., Fox, D., Thrun, S.: Coastal navigation – mobile robot navigation with uncertainty in dynamic environments. In: ICRA 1999: Proceedings of the IEEE Int’l Conference on Robotics and Automation, pp. 35–40 (August 1999)Google Scholar
  12. 12.
    Roberts, S., Guilford, T., Rezek, I., Biro, D.: Positional entropy during pigeon homing i: application of bayesian latent state modelling. Journal of Theoretical Biology 227(1), 39–50 (2004)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Bhattacharya, A., Das, S.K.: LeZi-update: an information-theoretic approach to track mobile users in PCS networks. In: MobiCom 1999: Proceedings of the 5th Annual ACM/IEEE Int’l Conf. on Mobile Computing and Networking (July 1999)Google Scholar
  14. 14.
    MacKay, D.J.C.: Information Theory, Inference & Learning Algorithms. Cambridge University Press, New York (2002)Google Scholar
  15. 15.
    Kuchling, H.: Taschenbuch der Physik, 17th edn. Fachbuchverlag Leipzig im Carl Hanser Verlag (August 2007) (in German language)Google Scholar
  16. 16.
    van Diggelen, F.: GPS Accuracy: Lies, Damn Lies and Statistics. GPS World 9(1), 41–45 (1998)Google Scholar
  17. 17.
    Timm, N.: Applied multivariate analysis. Texts in statistics. Springer (2002)Google Scholar
  18. 18.
    Capenter, B.: Arithcode project: Compression via arithmetic coding in java. version 1.1, online resource (2002), http://www.colloquial.com/ArithmeticCoding/
  19. 19.
    The OpenStreetMap Project, online resource, http://www.openstreetmap.org/
  20. 20.

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2012

Authors and Affiliations

  • Markus Koegel
    • 1
  • Martin Mauve
    • 1
  1. 1.Department of Computer ScienceUniversity of DüsseldorfGermany

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