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 state-of-the art compression schemes for spatio-temporal data.
Similar content being viewed by others
References
Baran I, Lehtinen J, Popovic J (2010) Sketching clothoid splines using shortest paths. Comput Graphics Forum 29(2):655–664
Bhattacharya A, Das SK (1999) LeZi-update: an information-theoretic approach to track mobile users in PCS networks. In: MobiCom ’99: proceedings of the 5th annual ACM/IEEE int’l conf on mobile computing and networking
Cai Y, Ng R (2004) Indexing spatio-temporal trajectories with Chebyshev polynomials. In: SIGMOD ’04: proceedings of the ACM SIGMOD international conference on management of data (2004)
Cao H, Wolfson O, Trajcevski G (2006) Spatio-temporal data reduction with deterministic error bounds. VLDB J 15(3):211–228
Capenter B (2002) Arithcode project: compression via arithmetic coding in java. Version 1.1. Online resource. http://www.colloquial.com/ArithmeticCoding/. Accessed 1 May 2012
Civilis A, Jensen CS, Pakalnis S (2005) Techniques for efficient road-network-based tracking of moving objects. IEEE Trans Knowl Data Eng 17(5):698–712
Creative Commons BY-SA 2.0. http://creativecommons.org/licenses/by-sa/2.0/. Accessed 1 May 2012
Fox D (1998) Markov localization: a probabilistic framework for mobile robot localization and navigation. PhD thesis, University of Bonn, Germany
Hönle N, Großmann M, Reimann S, Mitschang B (2010) Usability analysis of compression algorithms for position data streams. In: GIS ’10: proceedings of the 18th ACM SIGSPATIAL international conference on advances in geographic information systems
Imai H, Iri M (1986) Computational-geometric methods for polygonal approximations of a curve. Comput Vis Graph Imag Process 36(1):31–41
Koegel M, Baselt D, Mauve M, Scheuermann B (2011) A comparison of vehicular trajectory encoding techniques. In: MedHocNet ’11: proceedings of the 10th annual Mediterranean ad hoc networking workshop
Koegel M, Mauve M (2011) On the spatio-temporal information content and arithmetic coding of discrete trajectories. In: MobiQuitous ’11: proceedings of the 8th annual international conference on mobile and ubiquitous systems: computing, networking & services
Koegel M, Kiess W, Kerper M, Mauve M (2011) Compact vehicular trajectory encoding. In: VTC ’11-Spring: proceedings of the 73rd IEEE vehicular technology conference
Kuchling H (2007) Taschenbuch der Physik, 17th edn. Fachbuchverlag Leipzig im Carl Hanser Verlag (2007) (in German language)
Lange R, Farrell T, Dürr F, Rothermel K (2009) Remote real-time trajectory simplification. In: PerCom ’09: proceedings of the 7th IEEE international conference on pervasive computing and communications, pp 184–193
MacKay DJC (2002) information theory, inference & learning algorithms. Cambridge University Press, New York
McCrae J, Singh K (2009) Sketching piecewise clothoid curves. Comput Graphics 33(4):452–461
Ni J, Ravishankar CV (2007) Indexing spatio-temporal trajectories with efficient polynomial approximations. IEEE Trans Knowl Data Eng 19:663–678
Roberts S, Guilford T, Rezek I, Biro D (2004) Positional entropy during pigeon homing i: application of bayesian latent state modelling. J. Theor Biol 227(1):39–50
Roy N, Burgard W, Fox D, Thrun S (1999) Coastal navigation—mobile robot navigation with uncertainty in dynamic environments. In: ICRA ’99: proceedings of the IEEE int’l conference on robotics and automation, pp 35–40
Schimmelpfennig KH, Hebing N (1982) Geschwindigkeiten bei kreisförmiger Kurvenfahrt—Stabilitäts—und Sicherheitsgrenze. Der Verkehrsunfall 20(5):97–99. In German language
Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423
The OpenStreetMap Project Online Resource. http://www.openstreetmap.org/. Accessed 1 May 2012
Timm N (2002) Applied multivariate analysis: texts in statistics. Springer
van Diggelen F (1998) GPS accuracy: lies, damn lies and statistics. GPS World 9(1):41–45
Acknowledgements
The authors wish to thank Dennis Dobler for his work on the prototype of the arithmetic coder and the formal model. Also, the authors thank Bob Carpenter for the source code of his arithmetic coder and his support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Koegel, M., Radig, M., Hyko, E. et al. A Detailed View on the Spatio-Temporal Information Content and the Arithmetic Coding of Discrete Trajectories. Mobile Netw Appl 18, 373–388 (2013). https://doi.org/10.1007/s11036-012-0414-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11036-012-0414-y