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Calculation of the parameters of Hidden Markov models used in the navigation systems of surface transportation for map matching: A review

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Abstract

This article provides an overview of the mathematical methods for calculating the parameters of Hidden Markov Models (HMM) used in conjunction with the map coordinates measured by the global positioning systems (GPSs) of mobile navigation systems. These methods are analyzed and compared. There is considered an example of calculating of emission probability of observations emissions and transition probabilities for the Hidden Markov Model of a road network. The example is accompanied by the construction of a states diagram of the HMM and a trellis diagram of the Viterbi algorithm. Using the example, there is estimated the influence of the choice of the value of the standard deviation for the probability density distribution of the minimum distances and the angles difference between the direction of the road element and the direction of the velocity of the vehicle on the probability of the path on the Viterbi trellis. It is proposed to use the functional dependence of the optimal path on the standard deviations and the orthogonal distances for the correction in the process of testing and the practical application of the algorithm of map matching based on the HMM.

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References

  1. NCHR Synthesis 301: Collecting, Processing, and Integrating GPS Data into GIS. Synthesis of Highway Practice, Washington, DC: National Academy Press, 2002; http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp-syn-301.pdf.

  2. Hummel, B., Map Matching for Vehicle Guidance, Dynamic and Mobile GIS. Investigating Changes in Space and Time (Innovations in GIS), Drummond, J., Billen, R., João, E., and Forrest, D., Eds., CRC Press Tylor & Francis Group, 2006, pp. 175–186; http://www.mrt.uni-karlsruhe.de/z/publ/download/hummel2006b.pdf.

  3. Pink, O. and Hummel, B., A Statistical Approach to Map Matching Using Road Network Geometry, Topology and Vehicular Motion Constraints, Proceedings of the 11th International IEEE Conference on Intelligent Transportation Systems, Beijing, China, October 12–15, 2008, pp. 862–867; http://www.asmemesa.org/itsc08/ITSC2008/papers/0311.pdf.

  4. Ren, M. and Karimi H.A., A Hidden Markov Model-Based Map-Matching Algorithm for Wheelchair Navigation, J. Navigation, 2009, vol. 62, pp. 383–395.

    Article  Google Scholar 

  5. Krumm, J., Letchner, J., and Horvitz, E., Map Matching with Travel Time Constraints, SAE 2007 World Congress, Detroit, MI, April 16–19, 2007, paper no. 2007-01-1102; http://www.cs.washington.edu/homes/letchner/Papers/krumm-sae07.pdf.

  6. Rabiner, L. A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition, Proc. IEEE, 1989, vol. 77, no. 2, pp. 257–286.

    Article  Google Scholar 

  7. Rabiner, L. and Juang, B.-H., Fundamentals of Speech Recognition (Prentice Hall International Inc. Signal Processing Series), New Jersey: AT&T, Prentice Hall International Inc. Signal Processing Series, 1993.

    Google Scholar 

  8. Petrushin, V.A. Hidden Markov Models: Fundamentals and Applications. Part 2: Discrete and Continuous Hidden Markov Models; http://www.accenture.com/NR/rdonlyres/6EA0F25D-7FA7-4B43-AFDB-CBA983F1347F/0/HMMTutorialPart2.pdf.

  9. Holmes, J.N. and Holmes, W.J., Speech Synthesis and Recognition, New York: Taylor & Francis, 2002, 2nd ed.

    Google Scholar 

  10. Hidden Markov Models and the Viterbi Algorithm; http://people.ccmr.corneIl.edu/~ginsparg/INFO295/vit.pdf.

  11. Levy, R., Hidden Markov Model Inference with the Viterbi Algorithm: A Mini-Example, Linguistic/CSE 256 HMM Viterbi Mini-example, 2009, pp. 1–4; http://idiom.ucsd.edu/~rlevy/teaching/winter2009/ligncse256/lectures/hmm-viterbi-mini-example.pdf.

  12. Batzoglou, S., Hidden Markov Models and the Viterbi Algorithm, 2010; http://www.stanford.edu/class/cs262/notes/lecture6.pdf.

  13. Li Jia, Hidden Markov Model; http://www.stat.psu.edu/~jiali/course/stat597e/notes2/hmm.pdf.

  14. Murphy, K., Hidden Markov Model (HMM) Toolbox for Matlab. How to Use the HMM Toolbox. Computing the Most Probable Sequence (Viterbi), 1998; http://www.cs.ubc.ca/~murphyk/Software/HMM/hmm.html.

  15. Viterbi Algorithm; http://en.wikipedia.org/wiki/Viterbi-algorithm.

  16. Shokhirev, N., Hidden Markov Models. Algorithms (HMMcpp.zip + CppMatLib); http://www.shokhirev.com/nikolai/abc/alg/hmm/hmm.html.

  17. Van Diggelen, F., GPS Accuracy: Lies, Damn Lies, and Statistics, GPS World, 1998, pp. 41–45; http://www.gpsworld.com/gps/gps-accuracy-lies-damn-lies-and-statistics-1127

  18. Zelenkov, A., Kluga, A., and Grab, E. Accuracy Estimation of GPS Receiver Parametrs with Re-Reference System in Static Mode, Scientific Proceedings of RTU, Series 7, Telecommunications and Electronics, Riga: RTU, 2008. vol. 8, pp. 31–36.

    Google Scholar 

  19. Rousseeuw, P.J. and Croux, C., Alternatives to the Median Absolute Deviation, J. Am. Stat. Assoc., 1993, vol. 88, no. 424, pp. 1273–1283; http://web.ipac.caltech.edu/staff/fmasci/home/statistics-refs/BetterThanMAD.pdf.

    Article  MATH  MathSciNet  Google Scholar 

  20. Mahalonobis, P.C., On the Generalized Distance in Statistics, Proc. Natl. Inst. Sci. India, 1936, vol. 2, no. 1, pp. 49–55; http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA-1/20006193-49.pdf.

    Google Scholar 

  21. Groves, P.D., Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Boston: Artech House, 2008.

    MATH  Google Scholar 

  22. Hieu Huynh Quart, Thanh Vu Dinh, Ground Mobile Target Tracking by Hidden Markov Model, Science and Technology Development, 2006, vol. 9, no. 12, pp. 5–12; http://www.vnulib.edu.vn:8000/dspace/bitstream/123456789/1918/1/sedev1206-01.pdf.

    Google Scholar 

  23. Haversine Formula; http://en.wikipedia.org/wiki/Haversine-formula.

  24. Great-Circle Distance, http://en.wikipedia.org/wiki/Great-circle-distance.

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Authors and Affiliations

  1. Riga Technical University, str. Lomonosov 1v, Riga, LV-1019, Latvia

    A. V. Zelenkov

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  1. A. V. Zelenkov
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Correspondence to A. V. Zelenkov.

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Original Russian Text © A.V. Zelenkov, 2010, published in Avtomatika i Vychislitel’naya Tekhnika, 2010, No. 6, pp. 5–24.

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Zelenkov, A.V. Calculation of the parameters of Hidden Markov models used in the navigation systems of surface transportation for map matching: A review. Aut. Conrol Comp. Sci. 44, 309–323 (2010). https://doi.org/10.3103/S0146411610060015

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