Minimal Solvers for Unsynchronized TDOA Sensor Network Calibration

  • Simon Burgess
  • Yubin Kuang
  • Johannes Wendeberg
  • Kalle Åström
  • Christian Schindelhauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8243)

Abstract

We present two novel approaches for the problem of self-calibration of network nodes using only TDOA when both receivers and transmitters are unsynchronized. We consider the previously unsolved minimum problem of far field localization in three dimensions, which is to locate four receivers by the signals of nine unknown transmitters, for which we assume that they originate from far away. The first approach uses that the time differences between four receivers characterize an ellipsoid. The second approach uses linear algebra techniques on the matrix of unsynchronized TDOA measurements. This approach is easily extended to more than four receivers and nine transmitters. In extensive experiments, the algorithms are shown to be robust to moderate Gaussian measurement noise and the far field assumption is reasonable if the distance between transmitters and receivers is at least four times the distance between the receivers. In an indoor experiment using sound we reconstruct the microphone positions up to a mean error of 5 cm.

Notes

Acknowledgements

The research leading to these results has received funding from the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) within the Research Training Group 1103 (Embedded Microsystems), the strategic research projects ELLIIT and eSSENCE, and Swedish Foundation for Strategic Research projects ENGROSS and VINST (grants no. RIT08-0075 and RIT08-0043).

References

  1. 1.
    Birchfield, S.T., Subramanya, A.: Microphone array position calibration by basis-point classical multidimensional scaling. IEEE Trans. Actions Speech Audio Process. 13(5), 1025–1034 (2005)CrossRefGoogle Scholar
  2. 2.
    Biswas, R., Thrun, S.: A passive approach to sensor network localization. In: IROS (2004)Google Scholar
  3. 3.
    Biswas, R., Thrun, S.: A distributed approach to passive localization for sensor networks. In: Proceedings of the National Conference on Artificial Intelligence, vol. 20, p. 1248. AAAI Press, Menlo Park, CA, ; MIT Press, London, Cambridge 1999 (2005)Google Scholar
  4. 4.
    Brandstein, M., Adcock, J., Silverman, H.: A closed-form location estimator for use with room environment microphone arrays. EEE Trans. Speech Audio Process. 5(1), 45–50 (1997)CrossRefGoogle Scholar
  5. 5.
    Burgess, S., Kuang, Y., Åström, K.: Node localization in unsynchronized time of arrival sensor networks. In: Proceedings of 21st International Conference on Pattern Recognition (ICPR 2012), pp. 2042–2046. International Association for Pattern Recognition (IAPR) & IEEE (2012)Google Scholar
  6. 6.
    Cirillo, A., Parisi, R., Uncini, A.: Sound mapping in reverberant rooms by a robust direct method. In: IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2008, pp. 285–288, March 31–April 4, 2008Google Scholar
  7. 7.
    Cobos, M., Marti, A., Lopez, J.: A modified srp-phat functional for robust real-time sound source localization with scalable spatial sampling. IEEE Sig. Process. Lett. 18(1), 71–74 (2011)CrossRefGoogle Scholar
  8. 8.
    Do, H., Silverman, H., Yu, Y.: A real-time srp-phat source location implementation using stochastic region contraction(src) on a large-aperture microphone array. In: IEEE International Conference on Acoustics Speech on, Signal Processing, vol. 1, pp. I-121-I-124, April 2007Google Scholar
  9. 9.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24(6), 381–395 (1981)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Janson, T., Schindelhauer, C., Wendeberg, J.: Self-localization application for iphone using only ambient sound signals. In: Proceedings of the 2010 International Conference on Indoor Positioning and Indoor Navigation (IPIN), pp. 259–268, November 2010Google Scholar
  11. 11.
    Arun, K.S., Huang, T.S., Blostein, S.D.: Least-squares fitting of two 3-d point sets. IEEE Trans. Patter, Anal. Mach. Intell. 9(5), 698–700 (1987)CrossRefGoogle Scholar
  12. 12.
    Kuang, Y., Ask, E., Burgess, S., Åström, K.: Understanding toa and tdoa network calibration using far field approximation as initial estimate. In: ICPRAM (2012)Google Scholar
  13. 13.
    Kuang, Y., ÅAström, K.: Stratified sensor network self-calibration from tdoa measurements. In: EUSIPCO (2013)Google Scholar
  14. 14.
    Kuang, Y., Burgess, S., Torstensson, A., Åström, K.: A complete characterization and solution to the microphone position self-calibration problem. In: Proceedings of ICASSP (2013)Google Scholar
  15. 15.
    Nawri, N.: Berechnung von kovarianzellipsen. http://imkbemu.physik.uni-karlsruhe.de/~eisatlas/covariance_ellipses.pdf (1996)
  16. 16.
    Pertila, P., Mieskolainen, M., Hamalainen, M.: Passive self-localization of microphones using ambient sounds. In: 2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO), pp. 1314–1318. IEEE (2012)Google Scholar
  17. 17.
    Pollefeys, M., Nister, D.: Direct computation of sound and microphone locations from time-difference-of-arrival data. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 2445–2448. IEEE (2008)Google Scholar
  18. 18.
    Schindelhauer, C., Lotker, Z., Wendeberg, J.: Network synchronization and localization based on stolen signals. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 294–305. Springer, Heidelberg (2011)Google Scholar
  19. 19.
    Stewénius, H.: Gröbner Basis Methods for Minimal Problems in Computer Vision. Ph.D. thesis, Lund University (2005)Google Scholar
  20. 20.
    Sun, Z., Purohit, A., Chen, K., Pan, S., Pering, T., Zhang, P.: Pandaa: physical arrangement detection of networked devices through ambient-sound awareness. In: Proceedings of the 13th International Conference on Ubiquitous Computing (UbiComp), pp. 425–434. ACM (2011)Google Scholar
  21. 21.
    Thrun, S.: Affine structure from sound. In: Proceedings of Conference on Neural Information Processing Systems (NIPS). MIT Press, Cambridge (2005)Google Scholar
  22. 22.
    Wendeberg, J., Janson, T., Schindelhauer, C.: Self-localization based on ambient signals. Theor. Comput. Sci. 453, 98–109 (2011)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Wendeberg, J., Höflinger, F., Schindelhauer, C., Reindl, L.: Calibration-free tdoa self-localization. J. Location Based Services 5(1), 1–24 (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Simon Burgess
    • 1
  • Yubin Kuang
    • 1
  • Johannes Wendeberg
    • 2
  • Kalle Åström
    • 1
  • Christian Schindelhauer
    • 2
  1. 1.Centre for Mathematical SciencesLund UniversityLundSweden
  2. 2.Department of Computer ScienceUniversity of FreiburgFreiburgGermany

Personalised recommendations