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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
Biswas, R., Thrun, S.: A passive approach to sensor network localization. In: IROS (2004)
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)
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)
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)
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, 2008
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)
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 2007
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)
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 2010
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)
Kuang, Y., Ask, E., Burgess, S., Åström, K.: Understanding toa and tdoa network calibration using far field approximation as initial estimate. In: ICPRAM (2012)
Kuang, Y., ÅAström, K.: Stratified sensor network self-calibration from tdoa measurements. In: EUSIPCO (2013)
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)
Nawri, N.: Berechnung von kovarianzellipsen. http://imkbemu.physik.uni-karlsruhe.de/~eisatlas/covariance_ellipses.pdf (1996)
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)
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)
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)
Stewénius, H.: Gröbner Basis Methods for Minimal Problems in Computer Vision. Ph.D. thesis, Lund University (2005)
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)
Thrun, S.: Affine structure from sound. In: Proceedings of Conference on Neural Information Processing Systems (NIPS). MIT Press, Cambridge (2005)
Wendeberg, J., Janson, T., Schindelhauer, C.: Self-localization based on ambient signals. Theor. Comput. Sci. 453, 98–109 (2011)
Wendeberg, J., Höflinger, F., Schindelhauer, C., Reindl, L.: Calibration-free tdoa self-localization. J. Location Based Services 5(1), 1–24 (2013)
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).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Burgess, S., Kuang, Y., Wendeberg, J., Åström, K., Schindelhauer, C. (2014). Minimal Solvers for Unsynchronized TDOA Sensor Network Calibration . In: Flocchini, P., Gao, J., Kranakis, E., Meyer auf der Heide, F. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2013. Lecture Notes in Computer Science(), vol 8243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45346-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-45346-5_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45345-8
Online ISBN: 978-3-642-45346-5
eBook Packages: Computer ScienceComputer Science (R0)